but in general Christianity gets a bye because it holds a position of power in the western world and it has encouraged its own spread into as many cultures around the world as possible.

But the same is true for eastern religions too. They have their own power centers, and encourage spread to other parts of the world. Christianity was certainly a minority for us.

I am not entirely sure what the difference is, but the difference seems rooted in the different world views. My wife is a Jain, and she loves it when particularities of her religion are coopted by the mainstream. They tend to see it as increasing their influence rather than as being diluted. (As her folks love to point out, the habit of not eating meat in Hinduism has its origin in Jainism, and so does the symbolism of color white for purity. The mainstream hinduism does not interpret these exactly as Jains do, but Jains (at-least those that are visible and vocal) in India seem happy that they are being used at all).

However, I have also found that even Indians who come to US seem to want their exclusive identity preserved, and complain about others coopting their identities, which seems rather different from the mainstream approach in India.

I will pass on the Islam prayer because I don't understand Islam mainstream even in India well enough to understand their response to some one else using it, but I have celebrated Bakrid, and my friends have always encouraged me to participate.