What if you are a sincere Christian, but outwardly you have to behave like you're a Buddhist/Muslim etc because of societal/familial pressures?I think there are two sides to this coin.
I couldn't publically proclaim my conversion by joining a Christian church when I first became a Christian. In fact, the first five years of my life as a Christian I still went to temples and sat in religious Buddhist blessing ceremonies with my family because it was required of me. For five years I lived an "outwardly" Buddhist life while maintaining a Christian faith secretly.
There is sense in attending these activities in order to maintain your relationships with family members and others. This isn't a bad thing and I have attended synagogue with Amybear and her parents several times. I'm sure I will again. They know I am a Christian, but they like having me go with them. It also often gives us opportunities to talk about our faiths that we would not have otherwise. So obviously I won't condemn this behavior. Biblically you have the freedom in Christ to do this and in the end, what you are doing is not so much about worship as about relationships. Plus it opens doors and gives you an opportunity to be a light to your loved ones. I think the passage Paul wrote in Corinthians applies here. Don't make others stumble and you'll be ok.
As in Messy's case I think adding her parents into the mix makes things harder. The bible says to honor them. You don't get to stop although an argument could be made if they attempt to compell you to break with your conscience.
On the other hand if you are concealing your faith from everyone in order to avoid conflict, well frankly that isn't a good thing. You aren't being a light to them or a Christian example, because you have hidden your light and they are ignorant of your faith. You are essentially denying your faith by going through the motions of this other religion. You are concealing the hope you have within you. The bible is full of people who have chosen martyrdom before doing this. You probably feel guilty about it and I think you should consider whether that guilt is the Holy Spirit convicting you of sin.
UPDATE: Let me clarify. I think that if you are in the second case, even if I were to say nothing about guilt, a person in that situation would still feel guilty. This is because they are doing something wrong (albeit under duress). But the thing to do is not to condemn that person, but to support them and build them up in love. Making the decision to tell your folks something they won't like is tough. Some people will need to mature spiritually before they have the confidence to take that step and you should be helping them to grow to the level that is necessary instead of tearing them down with even more guilt. In short, don't shoot the wounded.