In the NFL are players allowed to give the finger to anyone on the field ?
Nope. Major fines, expulsion from the game and bans from future game(s) can be the result. And they can't do it to spectators after the game either.
Wouldn't that be unsportsmanlike conduct? It is rude anyway.
No, that would be unsportsmanlike conduct.
It would result in a 15 yard penalty, as well as a possible fine and/or suspension from the league.