I understand this kind of question is going to produce lots of different opinions. That's the idea.
Tolkien is a good writer when we define 'good writer' as a writer whose stories are enjoyed by millions of people, or a writer who is capable of supporting themselves financially by writing fiction.
One of the definitions of good is 'having the qualities required for a particular role', which is pretty explicit in requiring someone to establish criteria with which you judge something as 'good'.
I think my answer to the OPs question is "yes".. but, just as I'm doing here, there are always detractors, and digressions available in these discussions.
What does that have to do with whether we can call Tolkien an objectively good writer? Just because you can't apply that to everyone doesn't mean that you can never tell.
In this case it's no longer about being "good", it's just about "how does it measure according to a rule?"
See Vincent van Gogh.
Much like there is no 'moral' without choosing a set of philosophical rules to measure against.
What's considered "good" also changes over time. "Earth is flat" was a "good" theory until people found out other possibilities, and so on.
Diving, gymnastics, figure skating etc. are in some respects subjective arts.
In the case of literature you can't stop someone from having a crackpot opinions such as "Tolkien sux because stories about 'other worlds' are escapist and distract workers from class struggles" or "I hate Tolkien because he inspired DanMachi and other sick anime that my boyfriend watches".
The value of Tolkien as a writer goes beyond "he sold a lot of books" to the influence he had with other writers. He was a pagan but certainly had common cause with his Christian friend C.S. Lewis when it came to the books they wrote. Whether or not you think Tolkien's influence is good or fair, it is objective that the influence was vast.
This gave me pause.
"Tolkien's Roman Catholicism was a significant factor in C. S. Lewis's conversion from atheism to Christianity, although Tolkien was dismayed that Lewis chose to join the Church of England."
 - https://www.wikiwand.com/en/J._R._R._Tolkien#/Religion
Tolkien was a pretty devout Roman Catholic 
If everyone agrees on what is being measured and how, then it should be easy to then do the measurements to get results. (who is best)
If the people involved in the comparison don't agree to a basis of measurement, then it's an exercise in futility and nothing more than an exchange of opinions.
In this sense, I'd posit "objectively good," is a question of beauty, and not measurement criteria. Those sports suffer from the Goodhart's Law problem (https://en.wikipedia.org/wiki/Goodhart%27s_law), where you don't need a competition to recognize someone is objectively good at something if they perform it beautifully.
The idea of "good," as a set of measurable scalar quantities presumes that you can express the object in those terms, which in the case of writing or a performance, you can't. There is no set of instructions that can reproduce a "real" performance.
You can produce something where people won't care about its difference from the "real" one (lots of economics and cog.sci on that one), but the existence of a simulation does not change the fact of the existence of the real.
For example, if some future GPT-7 produced the literary equivalent to crack cocaine, it would still not be Ted Chiang, whose work is beautiful and could be said to be objectively good. People might prefer this new crack-lit, which mutes their ability to sense ugliness, parasitism, disgust, or horror, but its existence does not obviate the existence of Chiang. That essential existence is what makes Chiang an objective phenomenon, and the beauty of his work is what makes it good.
I don't think there are short answers to this question though. :)
It seems reasonable to me to say that he is a popular writer and subjectively good and that he is an objectively good speller.
I'm not sure this is the case, at least not in English.
Which is correct: "color" or "colour"? They are both correct, of course, but for different dialects of English (en-US vs. en-UK)
Another example that I recently came across that is not dialect/localization dependent: what is the word for "able to be parsed"? Is it "parseable" (with an "e") or "parsable" (sans "e")?
While I've found some sources assert that "parsable" is correct - and I believe it is - others claim that they're both correct or that "parseable" is the correct form.
Suppose I'm working on optimizing a database. I add an index to the the columns `bar` and `baz` of the `foo` table. Have I added two "indexes" or two "indices"? While some sources say that "indexes" is an acceptable way to pluralize the word in English, they seem to all agree that "indices" is also correct. See: https://grammarist.com/usage/indexes-indices/
To make it more complicated, the link above states:
> [...] "indices" is generally preferred in mathematical, financial, and technical contexts, while "indexes" is relatively common in general usage.
Databases are certainly technical contexts... but I've never seen "indices" used in documentation:
For example, if we accept Merriam-Webster as our standard measure then in each case both spellings of color/colour and indexes/indices are acceptable. One might be preferred over the other but both are objectively correct.
We would then conclude that an author writing for a US audience (per the standard measure of Merriam-Webster) would not have erred in using colour (or color).
Does the ability to do something intentionally wrong for artistic reasons reveal that you are objectively less skilled at a task or more skilled?
And yes, it's possible. Am I objectively good at calculus? I passed the AP test. That's an objective measure.
But it's not that simple, for at least two reasons. First, it's always possible to question the "objective measure". Is the AP test a good test of whether someone is good at calculus? AP says so, but that's not actually any help. College admissions departments think so, too. But grad school admissions people don't think so at all, and neither do math department hiring committees. This shows the problem: There is a measure that can objectively be met or failed, but is it the right measure? How can you tell? Not objectively.
Second, in many fields, there is no analog to the AP test. Is Tolkein a good writer? Is the Mona Lisa a good painting? There is no clearly objective measure. The only measure is that many people think so; more people than think, say, my daughter's watercolor is a good painting. That's subjective, but at least it has the merit of being subjectively shared by many people. And with something like Mona Lisa, it's shared by many people across many years - it's not just today's fad. That's still subjective, but it's at least a subjectivity that has widespread agreement to it.
I think you've hit the nail on the head with this. Thanks for responding.
For example; a good movie can be subjectively bad (you didn't like it), but objectively good (great filmography, original plot, consistent story mechanics). And vice versa.
I suppose subjective criticism is like your gut-instincts, whereas objective criticism is trying to quantify metrics which explain these instincts.
Yes, I believe you can be objectively good at anything if you practice enough and receive feedback/make an impact.
Can you be a great writer if nobody reads your work? Can you be a great artist if nobody sees your paintings? ...... I'm not sure you can be honestly good at something if there's no audience to witness it......
In the classes I teach, I design the skills learned in terms of cash. A 3 day class will teach you enough to avoid paying a professional to do something, but not enough to get a job. A 3 month bootcamp will be enough to land you a nice job, but not $X salary.
With Patreon today, it's more directly correlated than ever. Even skills like birdwatching or poetry could pay out.
Take the example of spelling that another user brought up. They claimed it is objective, but that isn't really true. Is the correct spelling color or colour? The answer to that is cultural, and therefore subjective. Unless you hold as I do that popularity is similar enough to objectivity to qualify. The cultural or popular notion determine what is right regarding subjectively judged subjects. This notion, including the spelling and even usage of words, can change over time.
This argument doesn't really work; it would be equally valid if you rephrased the question as "is the correct spelling 'thing' or 'thnig'?"
There is a difference of opinion on 'color', and none on 'thing', but they're equally "cultural".
Sure, but it's not correct now, despite being cultural.
The "color" spelling is: (1) shorter: absence of the superfluous is better than its presence; (2) etymologically correct, since the Latin original is "color"; (3) closer to the spelling of the word's cognate in a bunch of languages: Spanish: color; Basque: kolore; Italian: colore; Polish: kolor.
For at least these three reasons, it can be regarded as correct.
English dialects that use "our" endings and whatnot should rid themselves of the baggage, except in the case of direct French loanwords like "velour", pronounced "..oor".
Firstly, I'm not aware of a documented "superfluus" usage in English. Maybe we have to go back more than seven or eight hundred years to find it?
Secondly, "-ous" (like "-ose") functions generally as an adjective-forming suffix and is derived from the Latin "-ōsus"; it does not correspond to, and is not an expansion of the the "us" ending in "superfluus". "superflous" can be regarded as a derivation of "superfluus" that has been regularized with the "-ous" ending to make it recognizable as an adjective. This has happened with other words, like "continuus" and "contiguus". In contrast to these, many "-ous" words in fact some from ancient "-ōsus" counterparts, like "numerous" from "numerōsus".
The case for reviving "-ōsus" in English isn't very good; since neither of its "s"s are silent, it calls for a change in the actual spoken words, rather than merely spelling. Plus, it is unfamiliar to English speakers.
The case for creating a class of "-us" adjectives to restore Latin spellings like "contiguus" or "superfluus" is also not very good. It may be shorter, but adds to the proliferation of suffixes. To retain the pronunciations, we need "uu" to be rendered as the diphthong /yuə/ or /uə/, the precedent for which is scarce (being apparently limited to just "continuum"?) I'm not aware of any dialect of English in which such a restoration attempt has taken place, unlike "color" and "neighbor".
The majority of Nazi Germany thought Nazi literature and art was good. Does that make nazi literature/art objectively good?
I'm no art historian, but I believe you just described Dada.
Only if there are established and accepted criteria, standards on which everyone agrees. The driving range of an electric car, for example.
By contrast, outside science and technology, "good" is a matter of individual taste.
My point? Standards must be defined and accepted by all interested parties.
Here's my favorite example of the opposite case: an optimist and a pessimist have a debate.
The optimist says, "This is the best of all possible worlds!"
The pessimist says, "That's right!"
Both declare victory.
However, you can choose a more objective formulation of what you want to achieve. One way is to express it in relation to what others do, e.g. "I won a marathon" - this is a proposition and an objective fact.
When we say someone is the best in their field, all we mean is that they seem to do something much better than everybody else in that domain or they possess some special quality that not many others have it.
Usain Bolt, Michael Jordan, objectively the best at what they do.
I think we can easily say these unbelievable athletes are "good" at their respective sport.
Not the lightest reading, but very worth the effort. TL;DR - taste is something that can be more refined or less refined. We have some reasons to believe that more refined tastes are 'better' than less refined tastes (people who have learned to appreciate more sophisticated tastes never want to 'go back' even though they now have fewer opportunities for enjoyment).
Obviously it's very controversial and you can make the argument that it's just snobbery, but I think Hume gets at something.
I would say that there are better and worse writers, and I can offer my reasons where I offer an opinion. Yet I know that there have been ages that reversed the attributions of better and worse held now. Shakespeare was out of fashion for a good part of a century, to name an obvious example in the English-speaking world.
Not if you're me.