what makes a true believer?

I have sort of a subjective definition of "True Believer", but to me, it's someone who believes in his/her religion adamantly no matter what challenges are thrown at them. In other words, they have absolute Faith in their own beliefs and they don't question it and they don't deviate.

As for following "the exact teaching of [one's] religion to be a member," it depends on the particular religion you choose. Excommunication is very rare these days. Most people don't really believe to the letter everything that their priests/ministers/rabbis/imams/kahunas or other spiritual guides try to teach; being a regular worshipper does not make one a "true believer."

And I would add to this that questioning and challenging the texts, ideas and beliefs of several major religions, in a way that is unique to the believer as a whole, is a key aspect of the faith itself.