You're right to say he's rebellious. But, I don't think he's religious.
In Romeo and Juliet, and all of his plays, Shakespeare avoids religious dogma. Instead, his characters are secular and humanistic, even the men of the cloth. It's as if Shakespeare foresaw the bloody struggle that religion would cause in England for the next century (Protestants versus Catholics; the Thirty Years War; Bloody Mary).
Friar Lawrence is more interested in healing naturally than spiritually. He's more into herbs and potions than chapters and verses. Sure, he uses some religious imagery, but it pales in comparison to all the flower imagery.
Friar Lawrence is more of a father figure to Romeo than a holy father. And since much of what goes wrong in the play comes from his bad decision-making, he's arguably not a very good father figure, either.