Jamal and Salim are Muslim. Their family was targeted by an anti-Muslim riot, and Salim is a Muslim name, and I think Salim said "Allah Akbar" once.
Is Latika supposed to be Muslim? She didn't wear a headscarf covering all of her hair, whereas Muslim women in most though not all countries do. On the other hand, there was a romance between Jamal and Latika, when Muslim men are only allowed to marry Abrahamic women.
It is not clear anywhere in movie to what religion she belonged. She was shown as orphan, it may be possilbe she never knew what religion her parents belonged to. As far as her name Latika is concerned, it is used by both muslims and hindus. It seems the director didn't want to show her as associated with any religion.
If you look at her life, most of the time she was in kind of house arrest, so she herself may not have had time to decide what religion she wants.
Regarding the logic that Muslim men are allowed to marry only muslim women, the society they belonged, I don't think rules are applied on them from any religous community. As Ankit pointed out in his answer, inter-religion marriage is not an alien concept, so she may be muslim or not.
Latika was not muslim. The name 'Latika' is prevalent in India for hindu girls, although this name is not very common.
Secondly, in India, several muslim men have married hindu women, so that is not an alient concept either.
