Is it grammatically correct and natural to say don't be being rude! when someone is being rude? I have heard people say something like don't be messing with my camera! when someone is messing with the camera, which made me wonder whether people say don't be being something. If they do, could you tell me it it's common.
don't be messing with my camera! is fairly common, but would be considered poor grammar at best in British English - other dialects maybe less so.
don't be being rude! isn't at all common, as Ronald says, you should just drop 'being' and go with
don't be rude!, which is by far the most common version of that phrase, or as second choice:
stop being rude!
It's grammatically correct. "Being" is a participle, which functions as an adjective, and "to be" can be applied to adjectives.
But I have never heard it before in my life. I've heard things like "Don't be messing with my camera,"—which is colloquial and dialectal, but again, 100% grammatical—but doubling up on the word "be" like that sounds very strange and awkward.
What I would say is "Don't be rude." In many cases, "You are ____" as opposed to "You are being ____" connotes that you are naturally ____ rather than just being that way at this moment, but the fact you're telling someone not to be rude implies that you think they are not an inherently rude person and that they're capable of being polite.