This research may be outdated at this point, but I read that parents have pretty little say over what their children actually become in ideology. Of course, the explanation was more complex than that, but I don't have the material on hand.
Regarding the political possibilities - well my parents were working class - father a carpenter and mother working in a hospital whilst I was growing up - such that both might be expected to support the leftist side (Labour here in the UK), but I'm not so sure about much of this. My father seemed to be more Conservative in older age, possibly something that this demographic is more inclined to, but can't say what my mother might have preferred. I have two brothers, the eldest seemingly being more right-wing (perhaps stemming from his inclination towards those with money), whilst the middle one perhaps was/is more left-wing (never really discussed such with him but he was more inclined to thinking), and I have always been more inclined towards the Left.
As personalities we varied quite a bit, which seemed to puzzle my mother at times, with my eldest brother perhaps being the most confident and me the least, with the middle brother being the most stable and least likely to get into any trouble. However, I did the best academically, even if I failed at this (given my potential), and the middle brother perhaps also, since he no doubt could have done better too.
Not really sure what our parents contributed, other than my mother seeming to me as being a lot more intelligent and wise than my father, and given what she apparently endured as a child, something rather remarkable to have overcome and to have dismissed.
As to any religious ideology, well my mother (and father, who just seemed disinterested) didn't seem to impose any particular belief on us. For which I am truly grateful - not that this would inevitably have determined such.
