In humans refined carbohydrates and hyper-processed food in general (which includes hyper-processed meat) contributes the most to inflammation.
Another studied suggests that meat intake increases levels of arachidonic acid, which is another mediator in inflammation and aging.
Those are just a couple of studies. There are plenty more where they came from. I highly suggest reading 'How Not to Die' by Dr. Michael Greger, to all those that are interested in way of reducing inflammation in the body. The book is incredibly well referenced, and a joy to read. 
Both those links are observational studies. The first link even admits that the association is weak. And the second link is a population-level study.
Observational studies are important clues, but too weak to base conclusions on, as in such studies it's hard to isolate the variables. For example given that red meat has been a scare crow, you've got the "healthy user bias" , in other words the people that tend to eat red meat are also those that tend to engage in unhealthy activities like smoking, eating junk food or not exercising. Scientists of course try to take such factors into account, but that's really hard to do.
Also such science is reductionist because it uses markers that may or may not have an impact on all cause mortality on or the quality of life, as such markers need to be read in context (often in relation to other markers). And since you mentioned "arachidonic acid", its rise isn't necessarily unhealthy.
Here's an article that debunks the notion that red meat is inflammatory: https://chriskresser.com/does-red-meat-cause-inflammation/
I get why people keep trying to fall back on Price’s research into the Masai, but I’m afraid it’s misleading. The Masai actually had significant rates of atherosclerosis, they just didn’t die from it, at least not the ones that otherwise lived long enough to matter.  To say that article 'debunks' it is disingenuous regardless. It is simply a counter-argument in article form; part of a debate that could well be retorted by someone more intelligent than myself (I'm sure Greger could give it a good rebuttal).
I think we can all agree that the best way to reduce inflammation is simply to exercise. It's been shown time and time again. By using the Masai as an ideal, we're simply looking at healthy user bias but in reverse. Justifying meat consumption with a tribal population that often runs marathons to catch said meat is baffling to me; it is not an excuse to dismiss a vast amount of research, both observational and otherwise.
I've latched on to meat and its markers of inflammation because it's relevant to the OP topic, but if we're going down the route of history, really we should be basing diet on our genetic biomarkers. "First of all, humans have been eating red meat for literally millions of years." should really be "First of all, small populations of certain humans have been eating red meat for literally millions of years." From my studies on ancestral human eating patterns, it seems that most were almost entirely vegetarian, and may have only eaten meat during celebrations a few times in a year. Scientific American had a great article on the topic .
To quote a favoured read of mine, "Human gene variants promoting veggie-rich and meat-rich diets are still distributed among modern humans. They fall into patterns one might expect given modern cultural dietary traditions. A gene variant that promotes conversion from plant based dietary food sources to omega 3 and 6 fats necessary for brain development is found more often in India, where many people are vegetarian. A different variant that slows this conversion is found among arctic people who eat a fish-heavy diet already very rich in these fats, according to a recent Cornell study."  This is why nutrition science is so difficult. However, I still believe that with the modern human exercising a little as we do - even 2 hours 7 days a week, a massive amount to us now unless you're an athlete, is very little compared to our meat eating ancestors - that a need for a plant based diet is higher than ever, and that applies to everyone.
Exercise helps, but the evidence for it is mixed. I don't think there's any amount of exercise you can do to undo the damage of a toxic diet, which the standard diet tends to be.
And as proof there are professional athletes that end up suffering from chronic illness and inflammation. Even more so, intense training like for running marathons can make you sick, because it can lead to a suppression of the immune system due to the stress involved . On a cursory search I found a meta-analysis on studies on the effects of marathon running on inflammation markers and the results are very mixed, endurance running promoting both anti- and pro- inflammatory markers. 
Therefore your claim doesn't stand to scrutiny, even though we can agree that exercise is mandatory for being healthy in general.
> "Justifying meat consumption with a tribal population that often runs marathons to catch said meat is baffling to me."
In your original comment you pointed at a population-level study (your second link). Why is mentioning a study on an indigenous population any less valid? Is that a double standard I'm sensing?
We study indigenous populations because chronic diseases are very modern and it has something to do with the modern environment, which includes the diet, especially since many of these populations got sick after being transitioned to the western diet.
The Masai might have been exercising more and live with less stress, which might have contributed to their overall health, or maybe they ate that meat with something else that reduced the inflammation, however this is an admission that context matters and that reductionist statements such as "red meat is inflammatory" are wrong.
Also apparently we burn as many calories as hunter gatherers , so I would be careful about such statements.
> "From my studies on ancestral human eating patterns, it seems that most were almost entirely vegetarian, and may have only eaten meat during celebrations a few times in a year."
The article you linked to is entirely devoid of any tangible proof and given the editorial style I can't take it seriously.
Indeed, the diet of apes and monkeys is composed of leaves, nuts, fruits and insects. However this is a very bizarre argument. Us becoming omnivores and starting to hunt animals and eat meat is what allowed us to adapt to harsher environments and to grow our big brains. Eating meat is what made us human and what drove us to develop tools made of stone for hunting or for collecting the bone marrow, it's what drove us to use fire for cooking, in order to increase the bio-availability of the meat and the starches that we eat.
First of all because our big brain can only be explained by the availability of high-calorie foods. High-calorie foods are not very available in nature in edible form. We couldn't have digested many of the high-calorie starchy plants that were available. The prevailing theory is that fire was first used for cooking in order to cook starchy plants that were toxic otherwise. But the first known use of fire was only 1 million years ago  and does not coincide with the expansion of our brains.
Use of stone tools however coincides with the expansion of our brains, yet routine use of fire may have began only 300,000 years ago , which means starchy plants weren't very available for us to eat, certainly not enough to explain our high-caloric diet.
The best indications for what our ancestors ate comes from looking at modern hunter-gatherers and we've got plenty of such populations observed .
Observed hunter-gatherers obtain most of their energy from animal foods . From the groups studied in that reference, they found ...
- 46 groups that obtained 85% of their energy from meat, fish and eggs (with no groups obtaining this much energy from plants)
- 133 groups that obtained 65% of their energy from meat, fish and eggs (only 8 groups that obtained 65% of their energy from plants)
- the median average obtained 70% of their energy from animal sources, 30% from plants
Note that this report has been criticized to have some flaws, but there is a substantial body of evidence for the theory that, on average, hunter-gatherers got 70% of energy from animals   .
 Cordain, L. “Implications of Plio-Pleistocene Hominin Diets for Modern Humans,” pp 363-383 in Peter S. Ungar, ed., Evolution of the human diet: the known, the unknown, and the unknowable, New York: Oxford University Press, 2006.
- The average human needs far more Omega-3 and far less Omega-6. Supplements of Omega-3 have been proven to help with inflammation (and heart disease, et al).
- Supplementing Omega-3 through fish oil or algae oil, etc. is proven to be effective, in a world where often times supplementation is not a substitute for diet.
- The Western world is less enraptured by spices and vegetables that are proven to reduce inflammation. I know this addresses your question, but does not answer it - there are many foods of this category. Turmeric, ginger, and maqui come to mind.
This is one of many considerations for our higher prevalence of heart disease.
- Supplementing extracts of anti-inflammatory/antioxidant plants has been shown to improve oxidative status in controlled studies.
- Diets low in carbohydrates have been shown to reduce inflammation.
^ I would share links, but I have hundreds of bookmarks and I wouldn't really know where to begin. I'd suggest just starting with searches on Pubmed or other scientific bodies and letting your exploration grow organically. It's a bit of a journey of understanding, and a whole lot of "what seems to make sense". Much of this stuff can not be proven except through trial - the fact of the matter is that there are too many intricacies, unless you care to devote your life to understanding it.
There are sure to be a lot of surprises in terms of what we have taken as truths, along with their dubious conceptions.
You might find studies that are counter to what I've stated, or it might be that your body composition doesn't respond as impactfully to these things as mine has. I am open entirely open to the idea that there are misfires in much of the research I have held dear. Only within the past few years has there been a concerted push toward studies on low-carb diets and the effects of inflammation, but they generally seem to point to these very important truths.
I am crusading a bit because I've been struggling with depression and anxiety my entire life - it took 27 years for me to consider that my diet might be the culprit, and with these changes I have an entirely new outlook on life. I understand that not everyone has these battles, and so do not need to seek these solutions.
But for those that do or must, it's been such a dramatic shift that I hope they will find hope in a possibility, that through research they can find a solution of their own. I never imagined that my mental health could be so influenced by my diet.
As they say (and which I never truly acknowledged): Your gut is a second brain.