You're trying to ignore "no laws respecting an establishment of religion" by twisting it around to mean the exact same thing as ,"or prohibiting the free exercise thereof." This is clearly wrong because it would be redundant. It would be like saying, "Congress shall make no laws prohibiting the free exercise of religion or prohibiting the free exercise of religion."
Congress shall make no laws respecting an establishment of religion. This means they can not create laws that pander to any religions or religious views, less it be unconstitutional. They are not allowed to create laws that prohibit, for examples, Christians from wedding only heterosexual Christian couples. But, at the same time, it is unconstitutional for Congress to ban gay marriage on the premise of Christian doctrine. If homosexuality is to be banned, they have to do it for non-religious reasons.