There is no actual halakhic obligation for even a Jew to wear a kipa. The brakha in the morning (which is to be recited upon doing the action) "`oter Yisrael batifara" is recited upon wrapping a turban. See Mishne Torah hilkhoth tefilla pereq zen. Over time in Ashkenazi galut, various customs changed and wearing a kipa became the accepted practice. This is good and fine, and proper. In fact, in tefilla, one should have one's head covered.
The idea of not walking 4 amot without one's head covered was meant as an act of hasidut of conversing with HaShem basically constantly. It was meant as having the head covered with a talith, as being in tefilla, rather than just walking about period.
There is no halakhic obligation to have one's head covered, besides for in tefilla. I know this response will not be popular, but it is indeed the correct understanding of the gemara and the actual halakhic requirement, contrary to popular understanding.
Our Arab cousins often share the same original style of dress as us in our originality, but it is distinguished other than through headcovering. Kipot and some other Ashkenazi dress sometimes originated from Christian sources. So I think the whole question stands on some misunderstanding to begin with.