Is it true the Catholic Church once performed same-sex marriages?
This is a common misunderstanding based on the ancient practice, mostly in the Christian East but also in the West, of "brother making" (adelphopoesis in Greek). This was a rite of brotherhood performed by a priest for two men, or even, more rarely, two women, or even sometimes for a man and a woman. Fundamentally, it was a consecration of friendship that carried with it certain obligations similar to being a godfather or godmother. There was never any notion during the centuries it was practiced that this was a "marriage" that would permit a sexual relationship between the two men or women.
Quite the contrary. The custom arose in the context of monastic life, especially of hermits and small monasteries (another indication that this was not meant to be a carnal union), and it spread to layfolk in their relationship to these monks, after the manner of the Western third or lay orders, only on a more individual basis. It also became a practice in military contexts. This was especially true in the Western Church in the Middle Ages at the time of the Crusades. In modern times it was preserved for the longest time among the Serbs and the Croats, Orthodox and Catholic, respectively. It is no longer practiced, despite calls for its revival.
The dishonest insistence of certain academic activists that these brother-making relationships were formally sexual, or a form of the very badly named "gay marriage," has been recently entirely discredited by a book, published by Oxford University Press, that documents the practice in the Christian East. Personally, I think it would be good to revive the practice in order to provide a counter witness to the sexualized gay marriage.
The Church surely blessed friendships between persons of the same sex, and Scripture and the lives of the Savior and his saints give us ample examples of this. Two men or two women are allowed practically every expression of mutual affection and devotion, except sexual intercourse, and we can teach this to counteract the notion that the Church cruelly rejects the emotional needs of same-sex friends.