^ There was never any theological justification for clerical celibacy. It was instituted in the 11th century purely to clamp down on priests inheriting their positions and thus reducing their accountability to Rome. It's entirely possible to lift the requirement tomorrow (which isn't the same for ordaining women to the priesthood), but this will cause a logistical nightmare within the bureaucracy. Their hand might eventually be forced, though.
Prohibitions on priests getting married go back to the councils of the 4th century, but those who were already married were allowed to become priests. The Roman Church commanded also that a priest live with his wife "as with a sister" and not have sexual relations with her. Unsurprisingly that was often not followed. At the 7th c. Council of Trullo the Eastern Church rejected completely the demand of abstinence for married priests. The Western Church eventually came to a different resolution, which was to prohibit the practice of ordaining married men altogether (and this was increasingly the custom for a long time before it became a uniform requirement in the 11th century).
There are theological and biblical justifications for the practice of celibacy for priests: the imitation of Christ's celibacy for the sake of his ministry & his bride the Church; Paul's advice to the Corinthians that "The unmarried man is anxious about the affairs of the Lord, how to please the Lord; but the married man is anxious about the affairs of the world, how to please his wife, and his interests are divided." But the practice of ordaining married priests that exists within the Eastern Rite of the Catholic Church means that the Catechism recognizes it as not an absolute theological requirement.
I wonder what is the effect for non-"straights" on the removal of the celibacy requirement. With this requirement, priests who are attracted to women are united in a common duty along with those who are attracted to men, and with everyone else. What happens then when the one group may take a spouse and engage in sex, and the other not? Does this solve a problem, or just divide relations among priests into subcultures?