Faith cannot be separated from the church by definition.
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Definition from Wikipedia:
The Church (from Greek Ἐκλησία, assembly) — a religious community united by a common dogma.
The key word is community. So it is completely unclear what prevents us from believing but not belonging to the community.
As an example: I am a big fan of Japanese animation, but once going on a march of the anime community and realizing that under this banner is just a crowd of people gathered to bustle, I do not go there anymore and do not relate to their community, while I continue to watch and love the anime.
So what prevents a man from believing in God, but not going to church and not counting himself to it? Especially if he thinks it is a rotten and corrupt structure.