The key thing now will be to see if there will be any exemptions allowed in society to a genderless definition of marriage. Will clergy who refuse to perform same-sex marriages be able to keep their ability to solemnize vows in the eyes of the state? I could see that changing in the next couple years.
Yes. If it is perfectly legal for clergy to refuse to participate in marriages that offend their values (one preacher that I know does not perform weddings in which the couple has cohabitated before the marriage within the previous year), it would be legal for clergy to refuse to participate in a same-sex wedding. Many are known to refuse to perform an interfaith wedding. Between a 90-year-old man and an 18-year woman? I'd have bigger problems with that than same sex.
The policy is set in part by a denomination, so one might have to ask of a denomination. I would guess that most Christian denominations would terminate the ordination of any preacher who refused to participate in a wedding solely because the participants are of different race.
There are civil weddings. Such is an alternative if local preachers object.