My dad and I have a positive relationship. I was briefly raised Catholic then raised Evangelical with varying degrees of conservativeness (my parents are not really conservative Christians but a huge chunk of the people I grew up surrounded by are). While I'm technically a Christian, I really don't speak about it publically nor do I attend church regularly and haven't for a long time. But I don't think the fact that I have maintained my faith (in what I choose, I am not a biblical literalist and I believe we cannot definitively ever fathom religion and God completely) is related to my dad.
Although, my attitude towards religion may partially stem from my parents'. We've always seemed to end up around people who are way more hardcore about faith, notice some form of hypocrisy, and disassociate ourselves as quick as possible. I think my parents may be (though ive never asked) in the same boat as me regarding religion.
I also had a year of very conservative Christian education, which also sort of turned me off. It was mainly a combination of Jesus in non-Jesus related things (like this is math class, we need to focus on math), things that made no sense (the earth being 6,000 years old, denying scientific theories without having reasons why they couldn't comply with the Bible, no critical thinking skills encouraged (which I realized in hindsight), and I felt that I couldn't speak my mind. Have you ever felt the wrath of a bunch of angry Evangelicals? I haven't, but it looks scary. I've also felt the wrath of angry Catholics (my extended family), and I frankly don't know which is worse. And for some reason I can never call anyone down (or use logic). I started to realize, "Wait , people actually think this? They're just not my parents who shrug it off and don't pay attention?"
I honestly think an education like that could turn someone into an atheist, probably moreso than a parent. Especially if they were exposed to it for a long time. That, or they will become essentially fully emersed in that interpretation.
Although, I still have one friend from back then and she is (as far as I can tell) a genuine believer in that particular strand of Christianity. Religion is important to her and it's helped her through hard times in her life. Interestingly, her dad was absent throughout a big chunk of her adolescence. He passed away when she was 16, and really had not been a very strong figure in her life due to his problems with drug addiction and depression for several years prior. If anything, I think that solidified her beliefs. Although, she and her dad were very close before all of the problems started. I'm not exactly sure how this has impacted her younger sister whose about 3/4 years younger. But her sister strikes me as someone more along the lines of my beliefs.
My parents are another interesting example. Neither had positive relationships with their parents. I do believe their parents cared for them genuinely, but were just too messed up to be positive influences in their childrens' lives. My dad was raised Catholic though I'm not really sure what my mom's religious upbringing was (from what I can tell, her family were not regular church goers). My mom became Catholic sometime in her late teens and she graduated from a Catholic University. She distanced herself from Catholicism and conservative Evangelicalism before my dad did. Her Dad fits the definition of absent/weak more than my paternal grandfather. Although he was present, he was just depressed, unemployed (not that there were very many good paying jobs available anyway, and smoked himself to death (my mom was in her early 30s when he passed though). I might sound a bit harsh on the man, but I never met him so maybe that's why.
In the end, it's different for everyone.