We can respect theirs and work together. Same with progressive Christians, Pastafarians, Satanists etc. I don't see any trouble as long as religious beliefs are not turned into "Rules to be followed by all".
You want to wear a headscarf... go for your life, you want to wear a cross... knock yourself out, A colander... hey no problem. Just don't expect it to be mandatory for all.
You don't believe in abortion... don't have one, you don't believe in homosexual relationships... don't have one, so on and so forth. Secularism is not that hard.
As it was said in the past, "Your right to throw a punch ends where my chin begins." I have no problem working with religious people who get and respect that. I have to bite my tongue a lot, but that's a small price to pay for the company.
Just a question... why do progressive Atheists, who are probably far outnumbered by progressive Muslims have to be the ones to make accommodations. Since when were progressive Atheists so powerful? Progressive Atheists are a weak minority, the only ally we really have is secular law.