Not that I care to speak about the man's family, but I believe that is the root of the rift between his parents. They are super religious and well with religion --- well with some you cannot question anything and must display blind faith.
Well, from the sounds of it, Aaron Rodgers is also religious... based on some of Rodgers comments (I believe from the time he did a podcast with Danica Patrick), it sounded like Rodgers was hinting at that he was not only New testament, but very new school of new testament (try your best and God will always love you and you'll make it into heaven).
Though at other time, his verbage has sounded almost more general spiritual and less clearly Christian (though that could simply be California new school Christianity)
Base to the podcast, where Aaron seemed to be hinting that someone else (not directly mentioned) that Rodgers has had some indepth personal debates with, truely and deeply believes in the old testament version of the Bible... (IT'S MY WAY or to hellfire and brimstone with you)...
And like you stated, especially the old testament you "cannot question anything and must display blind faith", ... follow or go to hell.
So based on that podcast, I think it's clear, Rodgers has a feud with someone that deeply believes the old testament, and he seems to be extremely new school religious.
Based on much much earlier comments from a number of family members (if I'm correctly putting it together, and I might not be)... I believe it's his Dad whom he is having issues with.
Which I thought became even more clear when his younger brother publicly attacked him for not calling their Mom when Aaron was supposively supporting donating and helping with the California Wild Fires... but he didn't call his Mom whom had to flee the home due to one of the fires. The brother attacked Aaron for not at least calling Mom... which to me implied, he understood why you didn't call Dad, but you should of at least called Mom. At least that's how I read into it. But this could be mistaken...