Fatherhood and motherhood need to be honored regardless of church affiliation or activity. One of the best Father's Day talks I have ever heard is the one that mentioned that we need to honor the fathers of our YM and YW (particularly) who are NOT members - or active members. We need to involve them, to whatever extent they will allow, in the discussions we have about how to help their children. I can't count how many times I've made that point in council meetings when someone says, "How can we help Johnny?" My response is almost always, "What did his father and/or mother say?"
By extension, we also should honor our own fathers in the same way - even if they were lousy fathers in most ways, and even if we are positive we will end up discarding their advice. We still should honor them as our parents who at least have the right to provide input.