How is it even constitutional for the government to be involved in marriage?

I've heard the argument that the denial of gay marriage is unconstitutional. But, I believe ALL government recognition of ANY marriage PERIOD is unconstitutional. First of all, it violates the Establishment Clause in the First Amendment. Marriage is a religious institution, so to have the government endorse it is an establishment of religion. Secondly, institutional marriage also violates the Equal Protection Clause in the Fourteenth Amendment. By giving federal benefits to married couples that are deprived to single people, single parents, and unmarried couples living together, the government is giving married people an unfair advantage under the law. The Constitution mandates that the government treat all people equally under the law, unless they have a compelling interest to do otherwise and the government DOES NOT have a compelling interest to treat married and unmarried people differently under the law. Thirdly, institutional marriage violates the fundamental constitutional principle of limited government. A government that's involved in our intimate relationships is NOT limited. So, let's return to the true Constitutionalism and get the government out of where it doesn't belong.