You will notice the debate is about tort/civil law, not criminal law.
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For example, Muslims could choose to have marital disputes or financial matters dealt with in a Sharia court.
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I definitely agree with this. If both parties agree to have it settled in a different manner, they are free to do so. Whether that's through a secular arbiter or a religious one doesn't matter. You can come to an agreement in civil law however you want. So the government offers a different marriage license with the note that disputes are settled in the Sharia court system for those who want it, or it's something the couple settles in a prenup.
In the US many types of contracts commonly include a waiver of a trial by jury and an agreement to settle any disputes with a private arbiter (selected by the company and who almost always rules in their favor). But as long as people voluntarily agree to it by signing the contract, there's no reason for the government to step in.