It depends what you mean by “conservatives.”
Real conservatives support traditional, morally healthy families and the right to life.
Why can’t they just live together like so many straight couples? No, they have to demand something they probably don’t even really want or need. One gay guy I talked to said he wanted to get married for the “dignity”. I always saw marriage as protection for the family, the obligation of the father to take care of the mother and children.
Actually it depends on what you think marriage is?