Well... that varies.
First, satire is less "mockery" and more "criticism".
Sometimes, like criticism, this can be more constructive, and lighter satire will focus on highlighting more universal human foibles, less mocking them and more "hey, see how silly this is? we act like that sometimes too, you know..."
This doesn't mean certain people who take those things very seriously won't still have objections to it, sure, but if you take the view that it's intended to shame those who are doing wrong and being willfully ignorant about it, you could say that they're calling for getting picked at.
The second part is it depends on how you look at the "harm" that is being done.
Many satirists would say their works are meant to be influential against problems they see in the world, corruption in church or state, human vices, the hubris of the elite... this might upset those people, but you probably wouldn't say that it's "harming" them unless you really think that's the way things should be.
Simply making fun of people, well... that's not really satire.
Some people, who say, make a movie with a lot of racist jokes in it, might defend the work by saying that it's "satire", but that's complete nonsense. So one shouldn't confuse the "I'm calling this satire as an excuse" brand of material with actual satire.
So satire shouldn't really be harmful in the first place. That doesn't mean some people won't take offense to it, or that it won't be done poorly and be intermingled with degrading jokes, but that's it's own issue, not something inherent to satire itself.
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