How do I approach him on Church teaching in a non-offensive way?
Never forget that he is still your father, and you must show him respect. Regardless of what religious faith he is, or non faith-Your father deserves you to respect. Unless he was abusive or something, show him courtesy.
The best thing to do would be "Hey dad, I found a great website (CAF) that really explains some Catholic teaching. Want to check it out?"
I'm not sure what you mean by "evangilizing about non-negotiables". Do you mean like "prolife" and "Sunday obligation"?
Maybe have a talk with your dad when the right time comes. Perhaps start by asking him his opinion on a topic, then inquire about his reasons for that opinion. Then you can come in with "But dad, I heard/read/learnt that...What about that?" You can't be dishonoring your dad by asking for his opinion. There's a way to do this without saying "but you must believe this" "you must do that". Remember, God has truth and if it is a non-negotiable, you should be able to defend your side with evidence.
I was born into a catholic family (well, half-catholic family, as Mom's at the United church). My sister and I got the full CCD up to confirmation, though my dad is by no means a conservative catholic. I'm pretty sure he has missed mass quite a few weeks in the past month or so (I am at the school teaching CCD when he used to go, and I think he's stopped).
I want to bring this up with him but it's important that we are charitable when we need to spread truth, whatever the truth is in your case. God is beauty, truth and love and we must never separate truth from love, or we make an idol out of the truth.
Just the :twocents: of a girl who spent her summer doing missionary work and evangilizing.
Does this make sense? Sorry if I rambled :blush: