No, this isn;t the theory that is going to potentially be useful to you. Nothing about your noise complaint requires you to believe or practice any religion.
What you have is a noise complaint. You will need to solve that through the local authorities -- police and City Councilperson can work with you to narrow the exemption, or by recourse to a nuisance lawsuit that tests the grant of the exemption. For a sound nuisance suit you will need skilled counsel.
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In essence you are complaining because the government has done nothing to prevent the church from amplifying the noise that reaches your home. They have done nothing to sponsor this noise. They have done nothing to violate the establishment clause of the First Amendment. You haven't said what the noise is. I suspect it is amplified instrumental music, probably familiar hymns. You would have better success filing to enjoin it as a nuisance, if in fact it is a nuisance.