Nothing.
There are married priests now. The Church has admitted many former Anglican priests that have sought to align with Rome many of them where married and continue to be married. The Church has allowed married priests in the past and may do so in the future.
The Church has never claimed that celibate Priests is a matter of Faith and Morals. No Pope has never spoken Ex Cathedra as to celibate priests.
Not talking about Anglican priests sneaking in the back door either.
The average Papist even know that the average parish priest isn't going to get married because the church frowns upon doing so.