Based on this:
http://www.migrationobservatory.ox.ac.uk/resources/briefings...
The majority of immigrants are likely non-Muslims. Only two Muslim countries appear in the top 10. Of the top 44% of immigrants, 8% are from two Muslim countries.
Likely a larger percentage of local non-Muslim Americans want to ban homosexuality than do immigrants to the UK. I wouldn't be surprised if in the US, immigrants are more open to homosexuality than US citizens.