A place of worship may have certain rules and customs, which others may not like to follow.
For example, the wife of Mr. Vayalar Ravi complained on NDTV program that she is not comfortable by the dress code (wearing a saree and so on) imposed by the temple. Today they will not like dress code, tomorrow they will not like Harathi and Sanskrit chants.
Moreover, we have very nice, pious Christians, who want to save all of us by evangelising us. Already they created nuisance near a few Hindu temples.
So, it is better to avoid complications. Let us not allow non-Hindus into temples.
Anyway, Christians and Muslims criticise "idol worship", "stone goids", "animal gods" and "superstitions" of Hinduism. So, why should they be allowed into Hindu temples?