This is a classic Chicken Little "the sky is falling" slippery slope argument, and like all slippery slope arguments is based on nothing but irrational fear. 

For generation upon generation Catholic priests, Protestant ministers, Jewish rabbis, etc. have been perfectly free to tell straight couples that for whatever reason they cannot be married in a particular house of faith. The reasons are myriad: incompatibility based on the cleric's assessment of the couple, the couple's failure to comply with one or more requirements as established by the church, synagogue, or mosque, or even if the cleric just doesn't think a couple is ready to make a marital commitment. No civil authority has ever censured a church for doing so in any way because churches have always had license under the Constitution to decide such things for themselves. 

What on earth makes you think any of that will change now that gay people can get married at city hall?