Right now we are getting the worst of all of it, we are getting the muslims and not the others. At least excluding based on natural origin would get rid of most muslims coming here.
If you have a better idea that will allow non muslims in and exclude muslims then great, let's hear it. But, Please be aware that most muslims will just lie and say they are nonmuslims if given a religion test.
Yes: your idea, but with an exception for refugee status for those with genuine well-founded fear of persecution as religious minorities.