Same-sex marriage is not a religious issue. It’s a legal one.
When you get married, you give your partner certain rights, and the two of you can act as one person. You can buy a house together and be treated as if you both owned it. If you have children together, you both get parental rights.
You get these rights because the government says you have them. No religious leader can simply point to two people and give them the ability to make medical choices for each other. The two people have to be adults, they have to decide to get married, and the person that marries them has to have been given that power by the government.
For the government to say that two people of the same sex can’t get married is like saying they can’t buy a car together. It’s an arbitrary refusal, a failure to fulfill one of the core functions of government: to enforce contracts.