No, it was only the 33rd Pope of the Church, Pope Siricius, who began mandating continence only in the 4th Century (which meant that 32 Popes before him were silent about mandated continence for over 300 years!); therefore, mandated continence is not an unchangeable Apostolic Tradition but a discipline of the Church which can be changed by the Successor of Peter who has the authority to bind and loose or competent ecclesial authority like the Holy See, Canon Law, and/or a solemn Council. When a married man is ordained through a dispensation from celibacy in the Latin Rite, that means he is thereby dispensed from mandated continence as well. A certain spirit of continence may be recommended, but mandated continence (which is a type of "backdoor celibacy for married men") is not required since continence is neither ontological nor essential to the priesthood. The Church has the authority to dispense with matters of discipline not essential to the priesthood. The Church taketh away, but the Church also giveth.
In 1139 A.D., the Second Lateran Council stopped admitting married men in the Latin (Roman) Rite priesthood. However, the Eastern Catholic Churches continued a non-continent married priesthood.
The Latin Rite began admitting married men to the priesthood in the 20th Century. Pope Pius XII first began dispensing married men to be ordained Latin Rite Catholic priests without expectation of celibacy-continence to celebrate the Traditional Latin Mass. Celibacy remained in absolute legal force in the West from 1139 A.D. to 1952 A.D.
Thus, mandated celibacy in the Latin Rite only existed for 813 years, but the married Catholic priesthood has existed for over 2,000 years of tradition since the Twelve Apostles.
The married Catholic priesthood has its roots in the ancient Order of Melchizedek, the married priest-king of Salem who offered bread and wine to Abraham. According to Oral Tradition and the Fathers of the Church as well as orthodox modern biblical scholars like Dr. Scott Hahn, Melchizedek was Shem, the son of Noah. Melchizedek had children which meant that Melchizedek was a married priest.
Support the return of married Latin rite Catholic priests in a way consistent with Catholic teaching!