You're going to get a lot of replies because this is an easy thing to have an opinion about. But the reason it is so is because it's incredibly subjective.
you mention that your father is the polar opposite of you politically. Well, so is my mum and she is my best friend for sure. She's ardently pro-brexit and I think it's stupid, we've even argued about it heatedly. (although often it can be quite "nice" to get an outside opinion, I am very aware of my own bubble and how the world has become this horrible polarising assortment of echo-chambers)
you mention that you have no shared hobbies, but that's not a dealbreaker either, I also don't have any hobbies shared with my mum.
The major difference might be that I have always had a "I trust you more than I trust myself" mentality, and I feel like I can tell her anything and not be judged. She doesn't have to give me solutions to every little problem but she will listen.
The other thing is I generally enjoy being in her presence, yes, she's overly tightly wound, she yells and gets aggravated to an unusually high degree, but she's a decent person and wants everyone to be happy, and that goes a long way.
What I'm trying to convey is that those things you mentioned don't matter as much as you might think they do, what matters is the kind of trust and enjoyment you both get out of each other generally.
I'm very bad at keeping in touch with people so I'm the wrong person to say that society expects you to call your parents. I don't think anyone outside cares if you do or not- it's about you and how much you want them in your life.