Jon cannot be....[SPOILERS MAIN]

A bastard.... there's a lot foreshadowing about him being a Prince, right from the first book when 'bastard' Jon is compared to the 'prince' Joffrey

He HAS to be legitimate and that's why I believe in the theory that Rhaegar annuled his first marriage... polygamy isn't mentioned in the doctrine of exceptionalism....annulment is the only way to make Jon unambiguously legitimate

And annulment of a consummated marriage is very much possible in westeros but people on this sub seem to hate the idea for some reason...I personally hope it happens