I don't want to keep going back and forth on this, and I'm not sure of an exact definition I can put into words. But I do want to know more about extreme views. By way of example, and I'll take Judaism only because I'm Jewish and don't want to comment on others' religions. But Judaism teaches to welcome the stranger. I would hope if there was ever a Justice Lemonlime I wouldn't base holdings on Jewish teachings, but I would come into immigration cases with those beliefs. As would that my atheist parents taught me that we have an obligation to look out for the weakest among us. Or that I have family members who were refugees after WWII.
I don't care whether a Jewish nominee goes to synagogue, how often they go to synagogue, their opinions of various Jewish beliefs, etc. But if there were somehow a nominee who was an ultra-Orthodox Haredi Jew, a sect in which men and women aren't even supposed to walk on the same side of the street, and which does not believe in reading books other than religious texts or using the internet or in newspapers, it would be fair game to discuss whether they believe women should be given equal access to education or whether they think government censorship of books that address homosexuality is okay or whether they would be able to rule fairly on cases involving First Amendment freedom of the press.
I'm not sure how to define where the specific line is, but there is a point where membership in a certain group, religious or otherwise, could have negative implications on someone's ability to serve as a judge, and when that happens, questioning them on extreme views is appropriate.