Being told that they're sinful and that their love offends God, and being told that their relationships are unworthy of the civil right that is marriage (not the religious rite that some people use to solemnize their civil marriages), can eat away at the souls of gay kids. It makes them feel like they're not valued, that their lives are not worth living. And if one of your children is unlucky enough to be gay, the anti-gay bigotry you espouse makes them doubt that their parents truly love them—to say nothing of the gentle "savior" they've heard so much about, a gentle and loving father who will condemn them to hell for the sin of falling in love with the wrong person.
The children of people who see gay people as sinful or damaged or disordered and unworthy of full civil equality—even if those people strive to express their bigotry in the politest possible way (at least when they happen to be addressing a gay person)—learn to see gay people as sinful, damaged, disordered, and unworthy. And while there may not be any gay adults or couples where you live, or at your church, or at your workplace, I promise you that there are gay and lesbian children in your schools. You may only attack gays and lesbians at the ballot box, nice and impersonally, but your children have the option of attacking actual real gays and lesbians, in person, in real time.
Real gay and lesbian children. Not political abstractions, not "sinners." Real gay and lesbian children.
The dehumanizing bigotries that fall from lips of "faithful Christians," and the lies that spew forth from the pulpit of the churches "faithful Christians" drag their kids to on Sundays, give your straight children a license to verbally abuse, humiliate and condemn the gay children they encounter at school. And many of your straight children—having listened to mom and dad talk about how gay marriage is a threat to the family and how gay sex makes their magic sky friend Jesus cry himself to sleep—feel justified in physically attacking the gay and lesbian children they encounter in their schools. You don't have to explicitly "encourage [your] children to mock, hurt, or intimidate" gay kids. Your encouragement—along with your hatred and fear—is implicit. It's here, it's clear, and we can see the fruits of it.