Do I think it's constitutional for a law to require a priest give up their ability to solemnize a marriage if they refused to conduct private marriage ceremonies between two homosexuals? Absolutely not.
Similarly, it's not constitutional to require a priest give up their ability to solemnize a marriage if they did conduct a privaet marriage ceremony between two homosexuals.
There shouldn't be a law concerning what private religious ceremonies a priest does or does not do as long as such ceremonies are not somehow a violation of another law.
I support this constitutional challenge. If a church wishes to privately marry two people of the same sex in a religious ceremony they should absolutely have the ability to do so without having negative reprucussions from the state.