'Drat' is one of many expletives, like 'darn' 'or 'heck', which are harmless replacements for more offensive swear words. 'Oh, drat!' is the sort of thing that a polite person might say in a moment of annoyance, when they break something, or realise that they have forgotten something, for example.
No, it's not rude at all.
Do I use it? No, I don't think I do. It's a little old-fashioned. But now that you've reminded about it, I might just start using it...