Yes we should, and Muslim refugees are also victims of religious persecution. Unfortunately, Trump's order says we only care about your persecution if you're in the religious minority in your country.

But this type of vetting is used all the time. Refugees that come to the US (and other countries, including my own, Canada), examine refugee claims using very similar methods.

If you are a minority (religious, ethnic, political) that is used as evidence of persecution and helps your claim for refugee status.