Somebody please correct me if wrong, but does not the catholic church have a few married priests under a special dispensation because they came from another denomination into the catholic church?
It is also important to mention, that the Easter Orthodox priests who are married when they take their vows, can not rise in the ranks to bishop. Those remain unmarried postitions.
In the Catholic Church, priesthood is actually a three-level thing: deacon, priest, bishop. These men have received a sacrament known as Holy Orders, and are called, collectively, clerics.
The celibacy of all ordained clerics in the Western church is what's known as a "discipline," --- a man-made rule ---not a necessary feature of the clerical state always and everywhere.
In the Eastern church, married men can become deacons and priests, but men who are already priests cannot marry. And if married priest becomes widowed, he cannot remarry.
In both East and West, bishops are chosen from among the celibate.
I would guess that in the Catholic Church in the USA, most deacons are married men.
Anyhow, as I said, clerical celibacy is a man-made rule in the West historically, and could conceivably change.
This makes the "married priests" question quite different from the other things that the self-styled progressives typically want to change, such as:
(1) the masculine nature of priesthood (no priestesses)
(2) the indissolubility of a valid sacramental marriage (no divorce/remarriage)
(3) the sanctity of marital intercourse (no non-marital intercourse, no contraception, no perversion)
(4) the sanctity of human life (No abortion, infanticide, euthanasia, suicide.)
The Church could change the unmarried priest rule, but not the other stuff. Because the other stuff is God-made. You can't change His laws any more than you could change the Law of Gravity.