But it should be stressed that this is no way a consequence a specific teaching that targets people with same-sex attraction.
The root cause of the trouble is the fact that the Catholic Church has consistently taught something that is always counter-cultural, difficult, and even quite radical. Namely that the only proper place for sexual intimacy is within a life long bond between one man and one woman for the purpose of raising children.
The Catholic Church teaches that gay sex is an act of 'grave depravity' and that same-sex attraction is 'intrinsically disordered'. How is that not a specific teaching that targets 'people with same-sex attraction'?
http://www.catholic-catechism.com/ccc_2357.htm
The point is that the identical moral reasoning process is being applied consistently to all people, namely, sexual activity is to be avoided outside of a marriage open to children. Gay people are not being targeted by some sort of religious moral carve-out.