Motto of the cultural Left: If you can't defeat your opponent, marginalize and silence him
Here's a great summary by Catholic Lane on the strategy of the matrimonially deconstructionist Left for advancing the cause of same-sex "marriage."
In a word: marginalize anybody who disagrees with you.
It's a classic Leftist tactic in the culture wars. Being aware of it and challenging it when it happens is they key to defeating it.
Remember: they'd rather spew hate-filled rhetoric about you and call you a hater than actually engage the issues.