It might not be exactly rude, but it can feel odd to get a request from a total stranger.
What I find very irritating are friend requests from people who may not be complete strangers (maybe we knew each other many years ago, or went to the same school) who assume I'm supposed to know who they are. I got one request from someone who went to my high school, but we didn't know each other, didn't have mutual friends, and I don't think we ever exchanged a single word. Maybe she's a very nice person, but I don't see the point in connecting with her.
Another request turned out to be someone I had known, but she didn't exactly go out of her way to make that clear to me. She's married, and goes by a name I never knew her by. She has no profile picture, and very little information available on her page if you are not already friends with her. And she sent no message saying "Hi, it's So and so, remember we were in Whatchamacallit club in high school together." I have no idea if she was being ditzy, or just assumed she's so important that I'd know who she was? I was able to figure out who she was based on her friends list and her occupation, but felt rather irked at having to do so. (OK, I didn't have to, but it was going to drive me nuts until I figured out!) So I did find this request somewhat rude.