Just as every other group in our society, the Catholic Church enjoys the same rights to hold to its beliefs, organize itself around them, and argue for them in the public square. This is guaranteed by our Constitution. This includes the right to teach what it holds to be the truth concerning homosexual conduct—and to act as an employer consistent with that truth—without the threat of government sanction.
The USCCB continues to oppose “unjust discrimination” against people with a homosexual inclination, but we cannot support a bill – such as ENDA in its current form – that would legally affirm and specially protect any sexual conduct outside of marriage.
Moreover, because the passage of such a bill could be used to punish as discrimination what the Catholic Church teaches, the USCCB has always sought as comprehensive a religious exemption as is achievable, in order to protect the religious freedom of the Church, and of all others who hold similar views. One partial solution to this problem is to apply Title VII’s prohibition on religious discrimination, which is already incorporated in the current version of the bill.
Source has the whole letter.
It's all so clear now! As long as someone says it's their religion that makes them discriminatory and hateful, well, that's a-okay!
EDITED TO ADD:
Andrew Sullivan is on the case with a cogent analysis. "It is a profound betrayal of the core message of Jesus: that the already despised should be embraced not stigmatized, that the victims of discrimination be protected not marginalized." Good stuff there if you want some further reading.
This letter was written by the USCCB, which only represents American Catholics, not all Catholics everywhere. So my headline "The Catholic church has come out swinging against ENDA" was inaccurate and wrongly encompassed every Catholic in the world. Ongoing clarification in this thread, if you're curious. (Thanks, teh_elb.)