No, one cannot be a traditional Catholic and believe it is okay to have married priests.
By definition, a traditional Catholic believes that the discipline of celibacy in the Church from the beginning is true, correct, and should continue as the tradition. Traditonal Catholics are for tradition.
As G.K. Chersterton said, that in regards to the matters of family and sex, the Church has red and white. Red for the sacrament of Marriage and white for the consecrated virginity of priests and lay men. There is no pink. You can’t have pink, the Church hates pink.
Yes one can be a traditional Catholic, because “Catholic” and “Traditional” don’t mean post Great-Schism medieval Latin Church. The tradition of allowing both celibate and married priests is much older than the tradition of a celibate only priesthood. Even in the Latin Church. Even if the Latin Church only “tolerated” married men becoming priests it was still part of the tradition. It is those who try to pass these priests off as some sort of second-class clergy that are breaking with Tradition, as well as belittling, those priests/deacons of the other Catholic Churches within the Catholic Church.
Why is it that some of us Latins seem to think or act as if by allowing a married priests there will no longer be celibate priests? The eastern Churches prove that is not true, and so do the oriental Churches.
It is also a fallacy to pretend that Latin Tradition starts in the medieval period, and that’s how many Traditionalist behave, even though they are willing to bring up earlier writings, when it suits their purpose, while ignoring other things that don’t.
Yes things have had a tendency to get extremely liberal, and this needs to be fixed, but when people blatantly create their own version of that which is Tradition/traditional within the Church or the Latin Church there is always fallacy.
As much as I respect Chesterton, he is not an ultimate authority on this, and he is certainly not above the Pope. The Pope is also not above Tradition, and from the earliest traditions of the Church there have been both Married and Celibate priests/deacons, and to deny it or say it is wrong is to deny Truth and Tradition of the Catholic Church and all its particular Churches including the Latin Church.
And obviously the Church doesn’t “hate pink” or it would never have “tolerated” married priests.