In the USA there is no federal Constitutional Right to same sex marriage. The federal Constitution grants the right to govern, be left with indivudual states, so these laws are decided in 50 different States, not the Federal laws. There is an argument as to the the Constitution and definition of the "Pursuit of Life, Liberty, and happiness", if same sex marriage would be implied within this Constitutional promise. I do not know if that is something the Supreme Court will decide or not. So far the Federal Government has passed the ball on this issue, and left it up to indivual States. That was also the position of the Supreme court over the Gore election, to back the Constitution granting States the right to govern themselves, so refused to overturn the Florida Supreme Court decision backing the Gore ballot count judgement.
Individual states make there own laws concerning the criteria for a marriage licence. A few states have allowed same sex marriage, most states allow only same sex civil unions. At least 4 states voted this year to further define marriage as between a man and a woman. State and federal laws in the USA can not order any religion to allow these laws that conflict with their religious beliefs. That would clearly be a violation of Religious freedom. Even if a state allowed same sex marriage, it would be a legal marriage only, and they could not force any religion to preform the marriage. They could be married in City Hall with a Justice of the Peace or a Judge.
I think you know the answer and where the beliefs are from within Christian Religions, Islamic Religions. I am not sure of the position of Hindu or Buddists concerning this.
The issue is clearly a conflict between Laws and the Constitution vs. Religous teachings. You can put it into the same kind of conflict of Abortion, Birth Control, and the Death Penalty. OUr laws may or may not support some of these issues, but religions do not.