As long as there are registrars available who aren't so fussy, it shouldn't be a problem.

These allowances for religious distaste for perfectly legal activities become a problem when no other service is available. There is the example of Christian pharmacists in the US, who won't prescribe morning after pills, and sometimes not even birth control pills (though none seem to have a problem with Viagra). People who live in urban areas don't see a problem, but it becomes a problem when the only drugstore in two hundred km. will not serve the needs of women.