1) Publishers should re-hire all the proofreaders they fired to cut costs. Because having typos all over the damn book makes you look like a fucking hack. Do that FIRST. If there is money left, hire folks for other specialty work. Nothing else will make up for slovenly work.
2) Anything that raises the book-production cost for the author is to be viewed with great suspicion. The more pressure applied to do this, the worse it gets. If you are a self-published author: hire an editor FIRST, for the reasons given above. But preferably, find first-readers, sensitivity readers, proofreaders, etc. from among your friends and audience who will do it for free or barter. You can't afford to pay everyone, you're not a publisher. And publishers should not be fobbing off any of these costs on authors, if you're going through their house.
3) Awareness is good; censorship is bad. "This has problem X, so you might want to Y or Z to fix that" is valid writing advice. "You can't X" is horseshit. Of course I can X, I wrote it, didn't I? There's nothing stopping me from posting it either -- except if reader input indicates it might do real harm. I'm a bard. I do have to think about that, because my damage quotient is astronomically higher than average and I have mangled friends a few times. I learned to be careful about that. But at the same time, I don't want to sacrifice accuracy and diversity for the sake of political correctness. Some of my characters are assholes; some say offensive things; some just say things that are apt in context but someone feels that I personally have no right to write about them.
Fuck it. Writers gonna write. What you want to avoid is hurting people, especially if there's a way to accomplish your literary goals without collateral damage. In that regard, I have two pieces of advice:
* Know as many stop-tropes as possible, things like the Dead/Evil Lesbian. If you can write the story without the stop-trope, then do so. Use stop-tropes only as a last resort when the story depends on them. Know what you're doing. Include material to compensate for the damage if possible; e.g. one lesbian dying or being evil is not such a big deal if many other characters are live healthy lesbians.
* Pay attention to your actual readers. Anyone can kibbitz and their advice is usually worth what they paid for it. Who is your target audience? Who is giving you prompts/money? Who has the trait(s) your characters do? Those are the voices you should be listening to. They have weight.
4) Some topics and techniques are just plain controversial. They need stories too. Fortunately, the bottleneck is long since broken; publishers can no longer control what gets published, only what they choose to publish. You want to write something likely to piss people off? You have the whole internet in front of you. Use your power wisely.
5) The best way to fix the sensitivity issue is to hire diverse authors. There really is no substitute for this. It's great to have writers of any stripe portraying an ensemble cast of diverse traits. But you need trait-having authors for accuracy and insight. They will just plain know things that don't hit secondhand information. Hire women writers, people of color, disabled writers, neurovariant folks -- they all have different stories to tell, and the amount of ism damage done by internalized oppression is consistently lower than the amount done by prejudice from the privileged groups. Ideally, try to find people who already fixed their shit and can write trait-having characters without that oppressive baggage getting presented as normal.