Let's look at that:
Nazis: made it mandatory for homosexuals to wear badges identifying themselves as gay.
Christians: Say it's wrong to identify yourself totally with your sexual appetites.
Nazis: Hold rallies and make speeches full of hatred against gays
Christians: Organize "Hope and Healing" conferences.
Nazis: Force gays into prisons, concentration camps, torture.
Christians: Provide compassionate care for AIDS patients (e.g. the Catholic Church is the largest provider of charitable services for AIDS sufferers in the world.)
Nazis: like their founder Adolph Hitler, wants homosexuals to experience despair, "no exit," death.
Christians: like their founder, Jesus Christ, want homosexuals (and all of us) to be restored to wholeness, to be transformed, to "have life, and have it more abundantly."
Yeah, that's historic resonance, all right...