word to describe weakening religious faith

Maturing?
Waking up?
Wising up?
Seeing sense?
Using his brain?
Realisation?
Epiphany?

"He is backsliding" is a good expression, but as a rule usually used amongst Baptist. If he is a Catholic, Lutheran, Anglican or member of a mainstream church the word backsliding would as a rule not be used.
"His faith is getting weaker" would be better.

it may be said that "he has sobered up and is becoming drug free"

Doubt.

I hope our overseas poster understands our sense of humor.

Brain patient recovers from brain damage. Now believes in UFOs instead of religion.

BBB

Be careful what expressions you use to a foreigner regarding word to describe something in your language. What is fun amongst Americans can be very much misunderstood by a foreign person and he/she might get into trouble.
To say a person is maturing because his religious faith is weakening is an opinon and not a fact. We do not know the rest of the story.

It's a good question. I'm not familiar with a single word which summarizes a state of "weakening faith".

However, the terms Disenchanted and Disillusioned apply in a more general sense, and come the closest in meaning.

You could say, "He has become disenchanted with his religion", or "He is becoming disenchanted with his religion".

Look up the word 'apostasy.' It might fit what you have in mind. An apostate is a person who once embraced a faith but has 'backslid' and no longer believes. In the old days in Europe, an apostate would be burned at the stake for his/her apostasy.

I like Drewdad's "doubt": "He's beginning to doubt his faith", and so on...