The equal treatment of persons is, for the most part, supported by religion, but traditional Christians tend to accept moral restrictions on sexual activity, and it might be that if you are gay in orientation, Christianity requires you morally to be celibate. It also require you to be celibate if you can't find a marriage partner, even if you are heterosexual.
Christians might say this: whether you are gay or straight does not mean God is against you. It just means if you are gay, you can't have a moral sex life. But being heterosexual doesn't guarantee that you can have a moral sex life, either, so why is this a prejudice against homosexual people?
To go from opposition to homosexual activity to prejudice against homosexual persons, additional steps in the argument are needed.