You are asking to deny legal rights afforded to married couples by the government to gay couples. These include laws of inheritance, hospital visitation/medical decisions etc.
Now, you are allowed to have problems with homosexuality. I don’t support homosexuality. Nor do I support Messianic Jews or Christianity. I do support their legal right to their freedoms.
Why do I compare it to blacks and women? Women used to be thought of as inferior – including intelligence. They were discriminated against because of that. I am happy that the law reflects anti-discrimination. I can’t imagine asking to allow discrimination of others to continue.
How is allowing gay marriage infringing on your rights? You don’t have to accept them, you just have to recognize their legal rights.