Since you agree that marriage is a state/government contract if you will, why then should clergy have to perform it since the separation of church and state is what we have here. Apologies if you have already touched on this.
Re the bolded - clergy do not have to perform it at all. One (er, two I guess) can get married without any clergy involvement. The reason that clergy often (probably usually) do perform marriage ceremonies is inertia. It's the way it was done, and that goes back centuries. Since there are non-clergy options, and the First Amendment exists, there is no need to (unsuccessfully) attempt to force any clergy to perform any ceremony at all.