I take "consistent" to mean roughly "does not contain a contradiction", so "a belief that is consistent with reality" would mean something like "if you take all of reality as a collection of facts, and then add this belief, as a fact, to that collection, the collection won't contain a contradiction." It seems to me, if this is a fair representation of the concept, that some beliefs about the future are consistent with reality, but false. For example:

Humanity will be mining asteroids in 2024.

This is consistent with reality: there is at least one company talking about it, there are no obvious impossibilities (there are barriers, but we recognise they can be overcome with engineering)... but it's very probably false.