It's like the test that Harvard put out that shows we are all at least a little prejudiced. I was a little surprised by my results, as I'm racially mixed. I didn't want to admit it was true but I spent a while pondering and, indeed, I have my prejudices.
You're right. It's possible (but far from certain) that the NYT folks believe themselves to be more objective than they are (or are capable of being). But a delusional belief in one's own objectivity and aiming to tamp down on public shows of bias is not the same as the implication in the comment I was replying to (which implied a self-awareness of bias that was being intentionally hidden publicly).
You might consider reading "Manufactured Consent", by Noam Chomsky.
Chomsky's thesis doesn't suggest that entities like the NYT are intentionally biased and crafty in hiding it. His thesis suggests that the basic nature of news media as we know it, the economic models, social structures, etc. inherently work in a fashion that reinforces mainstream thought and rejects challenges to it.
I think Chomsky is right. My point is that the NYT is behaving exactly as Chomsky would expect including my suggestion that they aren't consciously aiming to be biased and hide it. They exist in a broader context where they can't even see their own bias (which is common in many cases, even outside of this topic of journalism).
In short: even when they present biased opinions as objective truth, they don't have whole meta-conspiracy around planning to do that. Nobody is writing these social-media guidelines thinking "this will better allow us to get away with presenting our political angle as objective truth" or anything like that.