I won't argue that homophobia and mysogeny are characteristics of some Arab Cultures.   But it's impossible to tell if that applies to immigrants.   If anything, they could certainly find a more agreeable place to stay than this country.  They are leaving violence, poverty, threat of death for a better home.  This isn't easy because of the huge differences is culture.   

And just as we have  American homophobia and mysogyny despite our civil law, there are Muslim people who reject homophobia and misogyny in their own country.   War does a lot of damage, immigrants certainly come with emotional baggage that can be difficult to handle.   I don't expect 'fuzzy bunnies' as you might say.   But I do support the healing of people abused by their circumstance and running from tyranny.