Is it okay / does it make sense for another player to join a running game of Munchkin?
I've played plenty of games where someone has joined mid-game, and it has worked very well them just starting as if from scratch (i.e. at level 1 and drawing the starting hand of 4 treasure, 4 doors).

In my experience, what tends to happen is the established players have no problem with helping them to fight monsters they can't beat, meaning they'll level up and get loot just fine without needing a level boost.

In terms of changing the play order, I have a feeling there's a card which influences turn order in one of the early expansion sets, something along the lines of "Player is now fighting this monster, and play continues as though this were the player's turn", effectively skipping everyone in between - although I can't find the card name or text with a cursory search. Also, I wouldn't have said Munchkin is a game which particularly relied on the turn order, so I don't really see how this could be a problem.

In my opinion, if someone gets upset over a new player joining mid-campaign in casual play, they're probably taking Munchkin too seriously.