Is it polite or impolite to resign on your opponent's turn?

Then you should quit chess.com chats and forums, cause you'll find that a lot.

Nothing rude about resigning whenever u want to. Ur opponent was rude for gettin all snooty over u not resigning. Nothing held up the winning move being played other than ur opponent wasting time typing a snooty response. Their rating doesn't matter. 

#4 what you said makes no sense. If formulating a response and calculating variations that are winning is a waste of time for you, than why do you still play chess? I don't understand. They are not irrelevant at all, you need to make those moves in order to win. Example I can think of is a game played between two super grandmasters recently, I can't remember which tournament it was, but one of the players was definitely Ian Nepomniatchi. Game ended by a draw even tho both players missed a winning idea. They thought position was drawn and repetead moves. Unfortunately I can't remember what he did, but Ian either gave his opponent a chance to win or miss his own. It was endgame with bishops and pawns if I remember correctly. It's almost always possible to recover after a blunder when your opponent doesn't take adventage of it, so you have to be on lookout all the time, there is no ring that signals when someone blunders, you have to notice them on yourself. If anyone knows the example I described please name the game, in the meantime I will look for it and send it here after I find it.

You should not resign on your opponents turn in case they don't notice your blunder. In this game, my opponent resigned because I can win material (the pawn is pinned to the queen so I win a rook) But i did not notice this. You should wait for your opponent to punish your mistake before resigning. And if they don't, you don't have to resign.