I'm in a religious country, and my religious supervisor is praying. What should I do?
I grew up in a Muslim-majority country. Do's and don'ts:

Do show respect for the religion. That means avoid doing things like comment on how inconvenient it must be to pray five times a day, don't offer non-halal food, don't invite people to lunch during Ramadan, etc.
Do do as they do, if possible and not inconvenient. For example if you take lunch together, order/pack something halal. Unless you have special dietary requirements that require you to eat pork, don't eat pork when with others.
Do dress conservatively. If your institution has a dress code, follow that. If you're female, you can usually refuse to wear the hijab if it makes you uncomfortable (depends on country however), but still dress conservatively - e.g. don't wear something sleeveless, and wear hemlines that go below the knee (this rules out wearing shorts in public).
Don't pretend to be Muslim. You can't fake it. Learning how to pray in the religion takes time; the chant is nontrivial as well.
Don't pretend to be Muslim #2: just as important, once you identify as Muslim you could be bound to obey a different set of laws. Sharia criminalizes things which are fine in contemporary Western culture, such as homosexuality. If you're homosexual but identify as Muslim, you could bring the religious police on your head.
Don't pretend to be Muslim #3: in some countries, if people believe you are Muslim, it can cause you a lot of inconvenience. It doesn't take much to become associated with the religion (extreme historical example, less extreme modern example), and once you become associated, it can be really hard to leave the religion. Potential problems you could face go up to death. In the meantime it's not just you that's affected: in many countries, there are restrictions on Muslim persons marrying a non-Muslim; plus any child born to a Muslim is automatically a Muslim.

Exception: if you were originally a Muslim but no longer believe in the religion, you don't have good options. The above advice will still bring the religious police onto you, because you're now an apostate. You would either have to pretend to be Muslim (at least you should know how to pray) or leave the country and work elsewhere.
tl; dr: Leave religious people to practice their religion and don't criticize them for it. They should do the same to you.