There are certain situations where I show tacit compliance with religious rituals. For example, when my Catholic friends invite me to dinner as they often do, I let them pray before hand and I am quiet while they pray. ( yes, they know I am an atheist and they still invite me)
Also, when attending a funeral, I do not argue philosophical subjects or condemn the proceedings in the presence of the bereaved.
If I were a woman, I would not go to a Muslim country for any reason.
I have numerous Buddhist friends and none of them ever kneel nor do they ask me to practice anything regarding their philosophical beliefs.
My father was Jewish and we ate bacon and ham a lot.
I attended a mass a few years ago to hear a beautiful Bach piece. I applauded and later complemented the musical performers that invited me and who coincidentally are atheists. We also went to a gay bar afterwards where the priest met us for a cocktail. (I know this sounds like I'm making this up, but it is true.)
As a scientific experiment, I have tried prayer. My results were exactly like every other honest person's... non-existent. Prayer has zero effect except perhaps on the psyche of the practitioner.
I have meditated to see if it has positive results... it does.
What I'm saying is; "It depends on the situation."
Since any "belief" I hold is based on facts, it cannot change except in the light of new facts. If the Large Hadron Collider at CERN discovers gravitons, the Higgs boson, higher dimensions or super-symmetry tomorrow, I'll believe it. In that sense, I go with that prevailing scientific tide. However, I could no more change my "belief" than I could stop the rotation of the Earth with psychic power.
Would I eat something repugnant because my social acquaintances were eating it? ... no.
Now, would I recant my beliefs if an inquisitor threatened me with torture? ... probably.
Christians are famous for extracting that level of "belief." That's one reason this whole religion thing got so out of hand. Torture or the threat of torture is real. Pain or impending pain can be a fact. As such, it can make "believers" out of anyone.
Beliefs cannot change, but behavior can change to suit circumstances. Sometimes that behavior is simply social grace or respect for another's emotional state. Sometimes, behavior or professed belief changes because of sheer survival.
Facts do not require "belief." Until new facts are found, they remain facts. To the extent that my belief in facts affects my behavior; no, …my behavior does not change.
But I also recognize the "facts" of death, mourning or benign religious rituals. I wouldn't choose a funeral or pleasant dinner party to argue my beliefs. Those are inappropriate venues.
Unless threatened with pain, I would not adopt religious practices of any kind.
I do not and would not do anything unethical because a religious person asked me to. However, that really has little to do with religion. It is simply a fact.