I also spent a few years in a MENA country in an academic environment. As you say, eating food/drinking water in public during Ramadan was illegal, as were certain standards of dress, however my experience over the years was that this did not in any way mean that the individuals I lived and worked with (including those who were practicing Muslims) were by default unaccepting of my non-religiousness. I am curious why you say
Surely, if they know I'm "non religious" it will annoy them.
So even if my supervisor is kind enough as well as his other doctoral student, but they will be disappointed if he know my situation.
Perhaps you have more reason for believing these than you have included in your question, however, in my personal experience, none of my Muslim friends/co-workers ever expected me to conform to their religion. I certainly never pretended to be Muslim, and like other answers, suggest that you do not do this as this is likely to make the situation more awkward ('I converted to fit in' is probably not the best answer to give to an observant member of any religion).
My advice is that perhaps this does not need to a bigger issue than any other lifestyle difference that you might have with your co-workers, and not to read too deeply into it (as in assuming they have some kind of expectation of you), unless they give you reason for it. Government polices do not necessarily reflect individual expectations. By all means, if you feel unhealthy pressure or feel unsafe, don't stay. Otherwise, similar situations where there is a difference in lifestyle/culture between members of the group occur all the time.
Perhaps another group you join might go out regularly for coffee/alcohol when you are unable to join for dietary/religious reasons, or in another group everyone else has kids, so leaves early, or do play-dates on the weekend. But in such situations, the activity you have to miss out on is surely not the only way to build rapport/respect within your group and strengthen your relationship with your supervisor. So if there is no actual pressure for you to have the same religious beliefs, try to decide if you're bothered by their religious belief. If not, then focus your energy on finding some other topic/hobby that you have in common. If both you and they are respectful of differences, there may be no debate to 'open'.