It should not be based merely on taking their word. Any recent conversions would not be accepted either. There would have to be a relationship with an existing church and vouching from there as well as other people. Fox had a report on organizations with heavily documented Christians applying to be refugees. There are solid ways to prove it and anyone who is lacking solid proof would not be accepted.
So, this would be necessary for any person entering from any country? India? Germany? South Africa? Argentina?
What if the person just said “no” to “Are you a Muslim?” How does one prove one isn’t a Muslim?