Are there any lines in the play where the priest's gender is thematically important or commented on?
The priest's gender is extremely important because he can't perform the duties of a priest if he isn't male. That is what Shakespeare would have believed and he would view the people who changed the gender if his priest characters as heretics, as do many orthodox Christians today--hundreds of millions of them actually.
You realise the Church of England now has female bishops, yes?
And many Anglicans and former Anglicans view that as a massive heresy.
Shakespeare himself would have shared that view, and he incidentally may have been a secret Catholic himself, who do not have male priests.
Who cares? The head of the church supports it. ---