First, anything that happens in the community affects the children. If there is a liquor store in the common, it affects the children. If there is a church downtown, it affects the children. A community is a melting pot of all the local influences.
Second, let's assume for the sake of this discussion that I am against same sex marriage. The reason why doesn't matter. My children go to school. If they go to school with the children of a SSM couple, they are affected.
Regardless of whether or not you agree with SSM or homosexuality, it is a deviant behavior. As Americans, we accept many deviant behaviors. What happens in the bedroom, stays in the bedroom. When you legalize SSM, it's no longer staying in the bedroom. It's now in the community.