Only because people who believe that make it so. If they'd mind their own business and let people love who they want there'd be no issue.
On the broader matter of rights though, it appears from recent exchanges here that a lot of people don't really know what a right is. For something to be a right means you are entitled to act on it without the permission of others. I'd be very surprised if military recruiters could set up a booth on a university's premises without the university's consent, for example, so that's not a right. Similarly, you don't have a right to drive a car, get married, go fishing, or practice medicine. Anything that requires permission from others, like in the form of a license as those do, is not a right. Rights extend only to asking for the permission, there's no guarantee you'll get it.