Question: In the Orthodox churches I know celibacy isn't required of priests. But, I think in order to advance within the hierarchy up to like patriarch you have to be celibate. I may be wrong here.
It goes like this : Greek Catholic and Orthodox priests can marry, but they are banned from divorcing. Ergo, they have to really think it over when they decide to marry and have children with their wife - there is no backing out of it, they will have to make sure that they'll be happily married.
During the height of the 16th century Reformation in the Kingdom of Hungary, there were instances of Catholic priests misusing the chaotic characteristics of this period of religious quarrels, secretly or openly taking wives or lovers and founding families en masse as they wished, some of the bolder ones even several times over. There were several publicly-spread cautionary tales from the era which focused on warning the undecided parts of the Catholic clergy from breaking with centuries long traditions and adopting the more lenient, Protestant-style priesthood customs.
Then again, I've also read of the odd case from the 14th and 15th century, where Catholic priests had secret lovers or otherwise broke their vow of celibacy. One notoriously famous case occured during the reign of Sigismund of Luxembourg (IIRC) and involved a promiscuous priest from one of the smaller Spiš towns. His case was so outrageous for the era, that once the authorities found out, they made his life a living hell. While he was eventually pardoned, his whole career was ruined and he basically spent the rest of his life in prison and then in a monastery.
And even when the rules were nominally enforced, actual practice was sometimes .... looser.
People being people...
Im a descendent of jon biskup arason, the last rc bishop of iceland, descended through this father and his son, both rc priests and all nominally celibate!
Ha, so you do have Icelandic roots after all !

And you're even the descendant of a naughty-naughty bishop.
So when BISHOP can get away with this in the hinterlands, you can imagine parish priests in the boonies in england, say, did much the same.
Yeah, the examples from medieval Hungary that I've mentioned certainly confirm this tendency.