Of course reporting just this information is non-neutral.
Wouldn't not reporting that information also be non-neutral? As you are, from one perspective, hiding information that one side doesn't want to be shared, thus favoring their political stances.
Yes, not reporting that information would also be non-neutral.
You could have very bland neutral reporting by omitting information that offends both sides (as long as you do so in a ratio that is roughly equivalent to how it occurs in the firehose), and you could have extremely provocative neutral by similarly highlighting that information.
There will be times when one side's opinions are more in conflict with facts of current events than the other, so you probably won't be pissing off both sides equally (this is why my original comment was pondering that, in the current environment, a neutral source could not remain trusted), but if you truly act as a service to that strives to fairly convert the "firehose" to a "drinking fountain" then that's what people (or I at least) mean when saying "neutral source."
Wouldn't not reporting that information also be non-neutral? As you are, from one perspective, hiding information that one side doesn't want to be shared, thus favoring their political stances.