To some extent, in order to establish rapport and common ground, we need to find the equivalancies. There are some - and there is the Pauline imprimatur to that appraoch at Mars Hill. If St. Paul can commend polytheists for worshiping the Unknown God (even if in ignorance), than we can commend Muslims for worshiping the One True God of Abraham. The other stuff - fundamentally important - must be addressed, but that doesn't remove the commonalities between two monotheistic Abrahamic religions.
I see no hint in the letter that evangelism is the ultimate purpose. Perhaps it is, but if so evangelicals like Rick Warren are hiding that purpose behind some very liberal company that would probably have little interest in evangelizing Muslims. Paul’s approach to the Greeks is an interesting parallel - though I would note that Paul did not assert with the pagan Greeks a common theology of loving God and loving their neighbor, as it seems that these Christians have done.
Rather, this letter is more along the lines of “we’re all together on this, let’s be friends” rather than Paul’s appraoch - “You are clearly religious, let’s talk about what you don’t know.”