The thing about religion is that it is so varied and open for interpretation, each religion means a different thing to each different person and each person chooses what values they hold. It clearly says in the first testament that homosexuality is a sin so generally, it is assumed that Christians and Muslims would be against it. However, there are plenty of Christians and Muslims who do support homosexuality because there are so many other things Leviticus prohibits like haircuts, eating shellfish, etc. It's literally impossible to follow every single thing it tells you to do and many people believe these rules are dated and that if God made you a certain way, it is how he intended you to be and he would never punish you for that.
On the top of my head, the only religion that completely has no problem with homosexuality is Buddhism. Sexual misconduct is frowned upon but misconduct is the same between a man and a woman as it would be between people of the same gender.