In a democracy, you work to make your opinion heard and effective. If you have the opinion, whether based on religious or other grounds, that homosexuality may damage the overall morality of a society, then you would work to protect that society from what you would view as a potential issue. You would also support laws that would be a means to that end--the goal not being to put somebody else down but to uphold it. Therefore a person that holds such beliefs would support enacting a law that prevents something, even if it didn't constrain them in any way.
In a democracy, you work to make your opinion heard and effective. If you have the opinion, whether based on religious or other grounds, that homosexuality may damage the overall morality of a society, then you would work to protect that society from what you would view as a potential issue. You would also support laws that would be a means to that end--the goal not being to put somebody else down but to uphold it. Therefore a person that holds such beliefs would support enacting a law that prevents something, even if it didn't constrain them in any way.