If that’s true right now, which I doubt, it’s not typically true. The usual NYT frontpage is hardline neoliberal everything, with no time for anything left of centre. Socially liberal was once associated with the left (only for a certain part of history, I note), but it’s long since been appropriated by large sections of the right (and to be fair, some of them were always there, due to being a certain kind of libertarian).
Neoliberals don’t like Trump, but you don’t have to be remotely on the left to dislike Trump. Pretty much anyone who values good governance, including an awful lot of Republicans, don’t like Trump. Have you already forgotten how many major mainstream Republicans quit or disassociated themselves from Trump in the early days. Honestly, if you think “anti-Trump” qualifies as “Left” you literally don’t know what you’re talking about and are just demonstrating the problem. Half the Republican-voting FB friends I have via my wife’s extended family have gone from voting for Trump to hating him over the last few months, too. None of them are any less right-wing in their general views, but they hate Trump now (or at least no longer trust him).
Specific trumps general. That’s the rule. If a specific op-ed is insane bullshit (or spreads misinformation/propaganda/falsehoods), then the general rule that it’s helpful to have diverse opinions doesn’t apply. People are total hypocrits about this, note. If an article which was insane in the wrong way, i.e. calling for a communist take-over of the US, got written, the NYT would most assuredly just not publish it. But call for the military to kill US civilians for no particular reason? Oh that’s fine. Proving that they aren’t really following the principle you’re espousing.
The big problem with the NYT is that it presents itself as leftist in arguments, claims to be leftist, and that the US elites (and a lot of idiots too) treat it as leftist. But it’s not. Not even by US political standards. It’s aggressively neoliberal, and has been gradually leaning slightly right for a couple of decades, particularly as neoliberalism has been seen to have failed.
Bari Weiss actually referred to this, sneering at people under 40, and claiming they’re all weak and just want to feel safe, but she neatly called herself and similar people at the NYT “civil libertarians”, which is perfectly correct, and demonstrates well how she’s not on the left. Libertarian attitudes are common in the US centre and right wing, and purely civil ones are particularly common on the centre. It’s a core tenet of neoliberalism - this sort of extremist ideological individualism. We’re all familiar with it, I hope (“there’s no such thing as society” etc.).
The other problematic issue with this entire thing is that right-wing news sources, even the more responsible ones, don’t typically have any left-wing columnists/viewpoints (or have staggeringly few - or always hilariously, have some sort of libertarian who they claim is left-wing because he’s gay or whatever). So you have a situation where leftist and centrist papers do a “both sides” thing, but rightist ones just do a “we’re right” thing. This wasn’t true twenty years ago, and it’s still not completely the case, but it’s been increasingly the case. This is part of the underlying source of a lot of complaints. FOX News are interesting because they’ve improved on this somewhat lately, but through the 2000s they were very very bad.
When the NYT is seen as a bastion of “the left”, it pushes the whole Overton Window to the right in a dangerous way. The NYT is pretty good on very basic civil rights - free speech, protection from false imprisonment, self-determination, for US citizens (and to some US immigrants). But that’s not really a leftist issue, given the strong support a lot of the right has for much of the same (nor should it be a leftist issue). But Bari Weiss was right - it’s civil libertarianism, which is accompanied by fiscal conservatism and hawkish international behaviour. The NYT is very much pro-military-industrial-complex (something originally a non-partisan issue, Eisenhower coined the term in his warning to the future about it, but which now only the left and non-neo-liberals, i.e. old school liberals, oppose - even though most of the public opposes it) for example, very much pro-interventionist war, against a US NHS-equivalent or privatization in general, and so on. Any policy you could definitely say “socialist”, the NYT is against it.
TLDR: They’re hypocrits and they mostly suck because people represent them to be far-left, just because they are mildly pro-LGBT etc. (even most Republicans in the US now support gay marriage so…).
I wouldn’t worry too much, because she’d have a lot of higher-priority targets (and indeed probably does), but it wouldn’t, sadly be the first time (even in the last ten years) that a person with hundreds of millions has started abusing UK libel law to harm/silence people. There was some ridiculous issue with a wealthy construction guy (and possibly lord) who had a similar name to a pedo. Initially, some people thought they were one and the same, or related, and said such on Twitter. It rapidly came out that this was not the case, and peoples started correcting this. But almost instantly, the construction guy had the most expensive libel lawyers in the country send threatening letters to not only the people who made the mistaken claim, but anyone who re-tweeted them (including people saying that the person was wrong), or even a lot of people who didn’t do that, but just discussed it. The demanded money and apologies, or else they’d sue.
Now, normally in the UK, you’d just go to court, win, and you’d get your costs (or most of them). But UK libel law is super-fucked-up, and you absolutely need a proper specialist, experienced libel lawyer to defend you (especially with a jury involved), especially from the best libel lawyers in the land. And that means you’d be thousands of pounds out of pocket in short order. Even if you won (which you probably would), and got your costs, you’d have been down thousands of pounds for months or even years. So what do you do? Most people paid up and apologised (even though they shouldn’t have) because the sums demanded were less than the cost of a lawyer for themselves, and had they lost, they’d potentially have faced tens of thousands in costs (in reality most judges would have ruled the construction guy was being exorbitant and cut them down, but it’d still be thousands) on top of any damages. Some people just ignored it and nothing happened, but others ignored it and got threatened further, so ended up paying up even though they’d done nothing wrong. Personally I feel like this should have lead to the lawyers in question being disbarred, and other lawyers doing this sort of thing have been disbarred, but these guys are the best and know how to flirt with extortion and not cross the line.
Rowling’s case is particularly gross in that she carefully targeted a paper which she knew couldn’t defend itself, because it’s too poor. Nothing they said is different to articles that have been in some major papers, but if she sued the Guardian or something, she’d actually have to go to court, and she’d lose, even if she kept appealing, they could easily match her, because they have money set aside for precisely this bullshit and her case is incredibly weak (relying on a comparison to someone who isn’t even a convicted criminal or anything, just a composer people with some racist views). And it’s high-profile enough to make the news and thus scare others.
She is literally looking to achieve a “chilling effect” on criticism of her position. That is literally the goal. After complaining about precisely that. By doing this, she threatens all the less-than-national papers and bloggers and websites and so on. She doesn’t really threaten individuals (there are plenty who have actually libelled her under UK law), because that’s not going to help her and would make her buddies say “steady on!”, but she chills all the smaller news sources and strongly encourages them to simply not report on this.