Not sure what you want here, but no, I'm not going to stop close-voting questions just because they're dealing with hard stuff.
Sometimes these questions aren't perfectly phrased because the person asking is emotionally fraught.
That is a perfectly valid reason to write a question that's not up to par. But it's not a reason to not vote to close. In such cases, I'm willing to refrain from downvoting, but I am going to vote to close.
They're dealing with some hard stuff, cut them a little slack. I'm not saying that we shouldn't moderate, I'm saying that we should take our time and be kind when we do it.
Cutting them slack is wrong. May I remind you that you were also the person asking How should we address chameleon questions on this site?. To prevent a question about a difficult topic from becoming a chameleon question, the first thing is to close it to prevent half-assed answers.
Taking time to do so is wrong. If you see a question that should be closed, close vote it. If you're uncomfortable or find doing so harsh, feel free to leave a comment to sympathize with the OP, and give them as much guidance as you can on how to improve their question.
When we moderate things, as a community, could we make an effort to be gentle with people when the question asked calls for it?
Yes, we can make an effort. Not by stopping close-voting, but by leaving comments and helping the OP to make a good question that can get good answers. In the end, this will benefit both the community and the OP: good questions help us grow, and good questions get good answers that the OP might actually benefit from.
The site is still small enough that we have the time and ability to be patient with people when it calls for it.
That's exactly the reason why close-voting quickly is necessary. We are still small, we should be able to keep up with close-voting unfit questions. If we don't we get a backlog of questions that should be closed but aren't, befuddling our scope.
If questions aren't closed, OP's aren't pushed to better word their questions. This will leave a mess that gets harder to sort out the bigger it grows.
Be kind, but don't refrain from close-voting while doing so. A sympathetic comment and a close-vote are better than an answer to a bad question.