Being a Gay Priest = Non issue.
Being a Gay Priest and telling the church to adjust to you = Issue.
At best the argument can be made that any 'non-hetero-married' sexual relationship is for 'practical purposes' the same as a hetero couple shacking up (at best, assuming its monogamous and caring).
Even a priests in an active sexual relationships, gay or otherwise, keep their jobs, provided they keep things quiet. The 'hypocrite factor' is even small if they do proper 'penance' for screwing around outside marriage and while being a priest (The church has been dealing with this as long as it has been celibate. Provided the priest is not making other problems, it has usually not been a firing offense. (Sleeping with a nice widow in a caring relationship is not the same as balling hookers, which in turn is not the same as breaking up a family).
A good argument can be made that 'state sanctioned' marriage presumed to be based on 'love' is the same for any sexual orientation. But that view of marriage is an aberration (although not an automatically 'bad' aberration), even for heteros.
Marriage until a century or two ago, was about inheriting children, family property, and family alliances by blood, and NOT just for royals. Even peasant families that had land rights operated this way. This is why grandparents and parents told kids who they would wed. Personal affections WAS a priority, but it was about #3 or #4 priority on the list. Furthermore, there were some very good reasons for running things this way. Decisive and CORRECT reasons if you focus on extended family above personal liberty. This made marriage that could not produce offspring a rare exception (although not unheard of, as all those other aspects of property and extended family politics would be in play, and yes, adoption happened too, but WITHIN that framework).
This is why when you hear how 'non-family orientated' western counties are, it usually means your grandparents don't get to arrange your marriage.
But having said all that, in the eyes of history, WE are the strange aberration.
My own focus, as always, is individual free will. So for 'state sanctioned' 'partnerships', I am completely cool with new things, but it is not traditional marriage. But then, unless a family is being made, neither are hetero set ups. And telling a church that it is has ANY obligation to sanction such set ups, or even call them 'marriage', is flat out wrong.