https://www.whitehouse.gov/the-press-office/2011/08/04/presi...
And there's nothing legally wrong about blocking immigration from a certain country or countries. We could block immigration from Italy and Poland and it wouldn't be unconstitutional despite the fact that they are predominantly Catholic. The religious test itself is what's unconstitutional.
All we'd have to do is ask:
What do you think should be done with homosexuals?
What do you think should be done with Israel?
and we'd get more than enough information to keep 90% of a certain religion out of here, without directly doing that.
No. If you want to block people who say they are against homosexuality, that might be legal. If you want to block people who say their religion is against homosexuality, that's not legal.
The subtle differences matter. Similarly, if you're hiring for a warehouse job, you can discriminate against people who cannot safely lift 50lb packages repeatedly. You cannot discriminate explicitly against people in wheelchairs, even though that group in general will have a lot of trouble lifting 50 lb packages overhead.
http://scholarship.law.georgetown.edu/cgi/viewcontent.cgi?ar...
It is worth noting he has since backed (evolved if you will) that position down to "extreme vetting" to "certain parts of the world" (Syria, Iraq, Afghanistan, Libya, Somalia, Pakistan, etc.)