A bible puppet is someone who bases all of their life decisions and judgement on what they read in the bible, as if it's a literal set of rules. However, this causes them to miss out on certain fun activities and misjudge other, based on their upbringing or religious faiths.
Ned: Until this, I never thought Homer and Marge were bad parents, but now I know you kids need a less hellbound family!
Maude: I don't judge Homer and Marge. That's for a vengeful God to do.
Homer: Stupid Flanders! He's such a bible puppet.