In the hyper-sexualized society we Christians inhabit, chastity is as counter-cultural today as it was for the early Christians in the decadent Roman Empire.
Fr. Stravinskas refers to this article: “Celibacy and Priests with Same-Sex Attraction” by Ryan M. Williams.
“The Church has always counseled against ordaining those who have same-sex attraction.” On the surface, that would seem to be the case, but a bit of history and psychology might be helpful here. It is undoubtedly true that “the Church has always counseled against ordaining” not “those who have same-sex attraction” but those who act out that attraction. Indeed, “homosexuality” and/or “same-sex attraction” are modern concepts. Prior to the nineteenth century, those categories cannot be found. What made one be considered a homosexual was the fact that one engaged in homosexual activity. Does a man with same-sex attraction who marries a woman contract a valid marriage in the eyes of the Church? Canonical praxis would suggest an affirmative response, which is to say that his “orientation” may make his marriage to a woman more difficult but not necessarily impossible.
Are there however unresolved psychological issues that lie at the origin of the same-sex attraction, which would be an obstacle to effective ministry? This is not a question of a modern "identity" but rather of whether one is psychologically healthy -- even if it is a relative standard (and not the same as holiness or virtuousness) it would seem to be a necessary foundation for public ministry.
(As for the counter-example of the man with SSA who marries a woman -- could not the existence of SSA be later cited as a ground for an annulment, should "things not work out"?)