Aren’t they leaving to go pray somewhere else to not make you feel uncomfortable?

While I don't know your location, my default answer to this would be "no, you should not do anything that makes you uncomfortable and surely not pretend to be religious in front of your supervisor or anybody else". The nuances on how to deal with this might be easier to suggest if you give us some hint of your location. But, what I'm really interested in is your statement that "Surely if they knew I am not religious it will annoy them" - how do you know that? Have you seen them treat non-religious students unfavourably, is it your funded or unfunded assumption, or something else?

@Jon Custer it's done in a specific place, that's why

Do they ask you to accompany them? I'm trying to figure out why you are uncomfortable with them going to pray at the place to pray. So, it likely isn't that they are leaving to pray, it is that you are the one who does not do so, and you are wondering if that will affect your relationships in the group. Is there any evidence that there is a problem? If so, follow the advice below...

@penelope I am in a predominantly Muslim country, MENA .. And the fact of not being Muslim is not very welcomed in general .. I let you imagine that eating during the month of Ramadan is not legal, and that it can be a source of physical or mental violence in the street. 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

@Jon Custer No they do not ask me, but the fact that everyone leaves except me is uncomfortable, and I fear that it can have an effect on our relationship

Yes, I can imagine some of the problems you have to face (from your descriptions) - but I can't quite put myself in your situation or give advice. Maybe you can edit this additional information in (about location and culture; maybe the example you give places it all in good context) for more pointed answers. My experiences are from international labs with a big cultural variation - so religion has minor to no influence on the supervisor-student relationship (although we have one actively and openly practising faculty and only one such student, not working together)

I feel this question requires a much more precise location. Muslim countries vary wildly regarding the tolerance of non religious people. While in some of these countries it would be fine to "come out", in many of these you could be risking your life or your scholarship. So obviously whether or not talking to your supervisor is appropriate depends completely in which case you are. MENA is huge, so it does not really say much about which possibility you are in.

Are you native to this culture, or are you an international student or postdoc coming from a different culture? If the latter, then you may not realize that praying 5 times a day, at prescribed times, is a fundamental religious duty of muslims, and that's all they're doing. Also, non-muslims may not understand that many of the rules in muslim countries are aimed only at muslims, and muslims in fact tend to be rather tolerant of non-muslims. The koran has a lot of violent messages but also a lot about peace...tolerance toward non-muslims, violence mainly directed at people who wrong muslims.

Can't you just ask for their prayer schedule so you know when they are available? (or, there are apps that tell you the prayer schedule). Then schedule to avoid prayer times.

Does doing the exact opposite make you more comfortable? Your current situation is "They leave to pray, you feel uncomfortable". What if it now changes to "They take you to pray", how would that make you feel? You're probably tackling the wrong perspective with the problem.

Is this question about academia?

@penelope: No that is bad advice. One must consider the repercussions of publicly denying religion in countries whose population will react badly to it. One might even have to pretend to be religious to preserve one's own life, especially if one intends to eventually leave such a country. It is really a waste to sacrifice unnecessarily.

If you don't go pray with them, how did they not figure out yet that you are not religious? Do they think you pray alone at a different time?

I think we all deal with similar thing in some aspects, where we ultimately have to conform or else face prejudice which negatively effect our lives. I myself am religious but I seek to find how beleif in god makes sense today. To me a person who does not believe in god, is not a rational person. Why are we here? What is all this? That said performing a social ritual is just as irrational. There are no answers, yet. It's up to you how fast we develop the answers and often there can be costs of developing them. Some how the three major religions stories seem to capture this. Our struggles

@Orion "...Is this question about academia?..." Not really. More like workplace or interpersonal relations. Still it gets good answers.

Edited the title because your supervisor praying in a de jure religious country is much different that a secular one ... I still think the location needs narrowing down though.

I had to look this up, so others might also. You could edit in: MENA is Middle East and North Africa.

It's interesting to know what is your country in MENA? I'm from Iran and not a believer at all. In our country it is pretty common that people will not attend religious practices cause it's more politics other than religion itself... anyway, I assume you are somewhere in the arabic countries of middle east and the problem is if you are a muslim by born (it means you are muslim cause your father and mother are muslim) and you don't believe in islam, you will be in a really serious trouble. But again it depends on country you are residing but arab people are strict about these kind of things...

I'd recommend respecting their values while sticking to your own. I've found most people (majority or minority) understand that there are people with different beliefs, and they're mostly thankful when someone from outside their faith shows them respect. But, that really depends on your precise location.

this sounds more like interpersonal.stackexchange.com or workplace.stackexchange.com question. What is your desired end result? what do you want to happen?

Just "hang back".

@horsehair: Comments are for asking clarifying questions or suggesting improvements to the question, not for insulting people.

Intolerance is not a Muslim-specific problem.

While you're not a Muslim, you shouldn't pretend to be one. BUT - depending on how much time you plan on spending in this country - would it offend you to read a few books, or talk to the local imam? I'm not talking about converting, rather showing enough interest in the lifestyle to get on well with your coworkers.

Is this question not better suited for IPS SE? I see nothing academia-specific, the question is highly location-specific, and at least 50% of the answers seem to be from a widely divergent cultural viewpoint, so much so that OP is unlikely to be benefitted in any way. The fact that this question is retained here, and so actively discussed almost indicates a fetishization of a certain culture/region/religion. Expect better from SE. Voting to close.

Yes, because they are not allowed to eat (not even drink water!), and if they see you doing it, you are corrupting their soul. So they handle you like they would handle the Satan. It is very rational and obvious from their view, but not from yours. Btw, I don't think it would be really hard to follow, you can eat if they can't see you.