This is a really interesting question. My parents have changed so much since they were young, at least from the stories that they and others have described about them. They have considerably gotten much more conservative as they have aged. My dad even claims my mom is totally different now than when he first met her.
My mom I think is an ESFP, with a very strong emphasis on the S. She was raised in a very strict Jehovah's Witness upbringing, and later rebelled and spent her time living in San Francisco working, nightclubbing, and traveling. She was a very outgoing and carefree individual. Never wanted to get married or have kids. I honestly don't think we would have gotten along very well though. We have some things in common, but I am sort of the opposite of what she was when she was young. I am much too shy and not a party animal like she was, so being friends with her probably wouldn’t have worked out.
My dad was typed before, but he can't recall his typing. I'm not really sure what he is, but I think he is an ESxx of some sort. He was known to be pretty shy when he was young, but a major playboy. Now that I think about it, he and my mom were pretty similar. They worked, went clubbing, dated people, and just had fun. They never thought about the future, just always lived in the moment.
In general, I'd assume they would probably think I was a weirdo. The friends in their social group were all like them too. I'm just not the kind of person that goes out often, going clubbing like they did every week getting drunk all the time. So no, I don't think we would be friends.