Is this a rude or polite thing to say?

I voted “unintentionally rude,” but it can be any of the choices, depending on the dynamics of the group, their relationship with each other, and their individual personalities. Also, the tone it’s said in, etc. Jane could have made an honest foot-in-mouth error and realized it as she was saying it and sincerely said “No offense” to Jon. Jane could be in a group that teases each other, so it could be a bit of a friendly jocular barb if she knows Jon is not sensitive about it or doesn’t really have bad teeth. If Jane suspects Jon has the hots for her and she’s not interested in reciprocating, she might have intentionally said it in a rude manner to keep Jon’s affections at bay. It could be any of a number of things. Is Jane normally a dick? Is Jon a dick? Yadda, yadda.

But, generically, without any other information, I vote unintentionally rude.

I voted not rude as she is stating her preference and had at least enough empathy to realize that her comment might offend at the last second.

Several rules in baseball depend on umpire’s determination of intent. If an infielder intentionally drops a line drive in order to start a double play, the umpire may rule that the catch was made and the drop was intentional, and call the batter out an no runners forced.

Basketball has “flagrant fouls”, judged on intent.

Which is realty irrelevant to the question. The answer to the OP depends on whether the participants in the conversation are accustomed to speaking plainly without offense to each other. My best friend and I are always insulting each other.

Right. it’s about sensitivity which is never out-of-style. I think Jane’s terribly insensitive. What if Jon IS embarrassed about his bad teeth, and can’t afford to get dentures or to have them fixed? He’ll try to laugh it off, but spend the rest of the evening mortified.

Happened to me a couple times, from the same woman. I’m pretty short, and I get and accept that’s a dealbreaker for a lot of women (although I’ve dated women both shorter and taller than me). One friend, in whom I’d never expressed any romantic interest, once mentioned in conversation, “I’m only attracted to tall guys. Ha ha! Sorry, Dorkness!”

I was all, "yeah, ha ha!’ and moved on, whatever. A tiny bit thoughtless, but not exactly something to give a shit about.

She did it again about a year later–almost exactly the same comment. That’s when it went from being nothing to give a shit about to still not being anything to give a shit about.

“I could never date a guy with bad teeth.” Not rude.
“No offense, Jon.” Rude, because it translates to: “Jon, it’s my opinion that you have bad teeth.”