Is it considered rude to say stuff like "mate in 4" in a casual game, and are there rules against it in the USCF and other governing bodies? I would personally not do it because I would probably be wrong anyway and then I'd look like an idiot, but do people do it?

I did that once- announced mate in five. Thought I was the coolest man on the world- for a few seconds anyway 😵

If you turn out to be wrong, even if the mate is forced but in a different number of moves than you announced, you'll look somewhat foolish. So why even think of doing it? Let the moves speak for themselves.
In a tournament, it is definitely not allowed, because you are not allowed to speak at all, except to offer a draw or resign. (You don't even say, "check."😉 So announcing a mate in a tournament is against the rules.

We had this announcing business in another thread. Some were for it, some against it. I don't see any point in it, unless you want to humiliate your opponent as well as beating him. To some players it wouldn't make any difference anyway, they'd play it out, delaying the loss as long as possible.