Could you expand on this a little? It sounds like you're saying that its a good thing to probe nominees' religious views.
Let's run with your example of a Muslim nominee. Imagine somebody comparable to Amy Barrett -- solid educational pedigree, prestigious clerkship, by all accounts a good, distinguished law professor, etc. -- but who happens to be a devout Muslim. This hypothetical nominee has never decided any cases that raise odd religious issues, has never written any law review articles about injecting religion into the law or anything like that. He's just a Muslim who prays five times a day, fasts during Ramadan, abstains from alcohol and caffeine (legitimately disqualifying IMO but let's set that aside for now), took a pilgrimage to Mecca, etc. Are you saying that it would be reasonable and proper for folks to worry that this person wants to impose Sharia law? Or would you think that people who wring their hands over that issue were being a little xenophobic and weird?
Sharia law? No that is not reasonable at all. If they are a devout anything though, I think it is certainyl reasonable to ask them how their faith guides them in decision making in regards to the law.