I have been trying to find, without luck, the verse that talks about people believing but still not following God. I think it was the Pharisees in Acts. I just remember reading a passage and I was wondering if you knew of it. I am using word searches but no luck yet.
I believe you are trying to recall the passage about the leaders of the Jews. "Nevertheless even among the rulers many believed in Him, but because of the Pharisees they did not confess Him, lest they should be put out of the synagogue; for they loved the praise of men more than the praise of God" (John 12:42-43).
This can also be combined with James' comment about demons. "You believe that there is one God. You do well. Even the demons believe--and tremble!" (James 2:19). Faith alone is insufficient to save.