helloooo people.
before i say anything, not that this is totally necessary to what i'm about to say, but i'm a practicing catholic - and a proud one at that. my opinion on same sex marriage is not aligned with the Catholic Church, in that if i could vote (i can't because of age), i'd vote yes.
in a way, the Church has a responsibility to state their opinion on this subject because they administer marriages. of course, you don't have to get married in a church, but they were the sole administrator of marriages for a long time (or were they? a bit unsure). their stance has been marriage is only for a man and woman, and they continue to maintain that. the Church regards marriage as a sacrament, and therefore, something that is very sacred. because of this, they won't marry same sex couples because it doesn't align with their view of marriage.
as for other religions, they have their own opinions on same sex marriage, as they're other administrators of marriage. they may think of marriage of sacred, like christians. i can't tell for sure, because i haven't looked into it, but the idea of marriage as a sacred thing is probably commonly shared over these religions.
like aaron said, everyone has the right to an opinion. in saying that, for a solid 3 weeks or so, the priest at my local parish has been like "hey guys, remember to vote no in the marriage vote!!!!" and i can tell you for sure that people have been influenced by this. it's also important for them to remember that they don't have to perform marriage rites for same sex marriage... like if you don't want to, don't.
however, religions should respect the opinions of others because loads of people in the LGBTQI+ (is that what it is now? can't remember) community feel ostracised from the rest of society, thinking that people are so against them. and that's crap.
so yea. religions can say whatever they want to, but they should respect the opinions of others while saying what they want to say.