Giving into left-leaning fashions is bad not because of the "left-leaning" part; its bad because of the "fashions" part. It's lazy groupthink at best, and bullying people into conformity at worst.
Have you noticed how narrow and specific all of the rules for reporting have become? Do you honestly believe that leftism is defined by these narrow rules, many of which are changing rapidly?
No. Most left-leaning people don't believe this stuff (how could a normal person even change their beliefs from one day to the next?). They go along with it because either they are too scared of getting bullied themselves; or because it's mostly hurting the right, and they believe they can regain control of the discourse after the right is diminished.
But it's easy to destroy good discourse and hard to rebuild it. After the right gets marginalized, we won't go to open-minded chats over coffee among left-leaning folks. It will be these same horrible tactics over the most minor differences of opinion on the left. Proponents of socialized medicine will be doxxing proponents of Medicare for all. There will be no end to the ridiculousness.
> I should reiterate that this is not a right-left thing.
This very likely is a right-left thing:
* The NYT systematically avoided the term "torture" in everything except op-eds when describing the Bush admin's post-911 torture program[1]
It's difficult to think of a more dastardly use of political correctness than a newspaper employing a euphemism for torture that effectively softens the blow in their stories about a government torture program.
Obviously if you knew about this but still subscribed to NYT anyway while now unsubscribing for problems wrt left-thing political correctness, that's a "right-left thing." (And however bad we both agree their left-thing political correctness problem is, it can't possibly be worse than systematically dressing up torture.)
But even if you didn't know about it, it's still the same problem. At best your comment makes it seem like NYT gave in to its long-standing penchant for left-leaning fashions, and that ended up actually damaging its ability to do robust reporting. That interpretation makes a special case of the entire Keller period when the most important stories were scuttled in deference to the Bush administration. That period includes refusing repeatedly to run some of the most impactful stories-- like Jim Risen's on the Bush-Cheney domestic spying program-- because the government told them not to[2]. That period is in major "never forget" territory wrt to journalistic integrity.
Edits: clarifications
[1] https://www.theguardian.com/commentisfree/cifamerica/2010/ju...
[2] https://theintercept.com/2018/01/03/my-life-as-a-new-york-ti...