You have it exactly wrong, the 1st Amendment guarantees that people who practice Judeo/Christian or Muslim morality will not be forced to accept what their beliefs classify as an abomination punishable by death.
Nowhere in any part of the Constitution or Bill of Rights does it say Judeo/Christian or Muslim morality. It simply says "religion". You are not being forced to accept anything other than to coexist with other human beings who have different beliefs than you.
The first amendment gives the freedom of speech, yet it doesn't give anyone the right to not be offended by someone's speech.
The fact that gay people exist in the same geographic part of the world where you live does not by any means that you have to accept their lifestyle. Do muslims have to accept people around them eating bacon or drinking beer, even though in their belief system, that is an abomination punishable by death? Are you being forced to accept the Gaiaistic beliefs of native Americans, even though that would be considered worshipping false idols? Are you forced to believe that Joseph Smith made up some cockamamie story about gold tablets in a language only he could understand? No. But the Constitution guarantees everyone the right to believe what they want to believe without restriction or persecution.
The right to the free exercise of religion is a right bestowed to everyone by the first amendment. To deny anyone that right, whether you agree with their belief system or not is wrong as long as they are a law abiding citizen.
If you want to go the biblical route, please refer to Luke 6:31. "Do onto others as you would have them do onto you."