"Ask a vehement Muslim about the beauties of the American social experiment" - the fact that someone is a Muslim and vehement doesn't in itself tell you what they think about the American social experiment.

I'm sure you could find Muslims who would wax enthusiastically about the beauties of the American social experiment, just as you can found Christians who feel the same. And they'd probably point to ways in which some of its underlying principles reflect the values expressed in their Holy Book. (And in both cases the wisest among them might then go on to lament the ways in which it has been undermined and distorted and betrayed.)