Belief in God is rational.
Everything has a cause. So unless there is a first cause, then you would have an infinite regress. And then nothing could exist. Therefore there must be a first cause. Therefore God, the first cause, exists. QED. (You could prove the first step a priori that everything has a cause by noting that nothing can come from nothing. This makes it a priori, not just an empirical observation).
I have thought hard on the basic aspects Nachman from Uman and my basic feeling is that his advice and ideas are very valuable. It is not that all the groups founded that go by his name are very good but that he himself had very important ideas concerning Torah.
The main problem is that people generally associate his name with the groups that the Gra put into excommunication.
It is a problem that his good ideas get used to seduce and influence others to do bad stuff.