I think you are missing the forest for the trees.
If someone goes to a church/synaguge/mosque, and follows the majority of the tenants of that religion, does that make something OTHER than that religion if they do not perform perfectly?
If someone who is Jewish does something that is very much against the basic tenants of the Jewish religion, does not stop him from being Jewish? No, it does not.
If a religious CHristian murders someone , does that make him not a christian?? No, it just makes him not a GOOD Christian. Trying to put the word 'true' before it is just a destraction trying to distance
the claimer from the person who failed to perform up to expectations.