I play “Jew” all the time in Scrabble on Facebook and it takes it.
“Jew” is never a legal word in Scrabble, because it’s capitalized. When spelled with a lower-case letter, “jew” is officially accepted. However, spelling “jew” with a lower-case letter turns it from a noun or adjective into a verb—specifically it’s a racially offensive verb meaning “haggle.” Many game publishers thus put it on the list of officially-legal-but-banned-nevertheless words like n... well, you get the idea.
I have no idea why any program would accept “muslim.” I can’t see any evidence that there’s an accepted lower-case spelling.