As for girls and sports, sure, girls can/do play sports. I have this theory, though, that when you have a household of all one sex, you have an increased tendency towards "girly" or "boyish" behavior, because that tends to be what the kids have in common. One girl might like dolls and theater, another like LEGOs and dolls, another like dolls and riding bikes, but that means that they all have playing dolls in common, so there's an increased tendency to play dolls because you see everybody else doing it, and everybody can do it together, etc. Versus my SIL's household which has a lot of guns and shooting and sports and superheroes.
For a long time, it was me and my five brothers. I didn't get a sister until I was nearly 10. And the family was as you say--there was an emphasis on boy-related things. Just because there were so many of them. So dinner table conversation was about sports. If there was a conflict about what to watch on TV, my parents went by the "majority rules" rule. So there was a lot of sports on the TV, and I rarely got to watch the shows I wanted to watch.
And all the boys played all the sports, too. There weren't many opportunities for team sports for girls in the 60s, and I wasn't interested in them, anyway. But I was expected to be interested in watching all my brothers play all their games. Bringing a book to Little League games got me in trouble--but there were 3 or 4 games a week, what will all my brothers playing, and frankly, those games were boring.
Sure, I had dolls and I played with them. But the boys teased me about playing with "girly stuff." I also played with the Tinker Toys and Lincoln Logs and we all had marathon Monopoly games and built forts with the sofa cushions.
There was just more boy-oriented stuff around, the sports equipment, the toy trucks and Hot Wheels and GI Joe (the original one that was bigger than Barbie). The general conversation revolved around my brothers' favorite topics of sports and cars and war (Dad was in the Army). If I tried to bring up something else, no one wanted to talk about it. And even if I wanted to do some of the things my brothers were doing, I was told, by adults and my brothers alike, that I couldn't do them because I was a girl. (Which didn't always stop me, if I wanted to do something badly enough. I was not a model child.) And a lot of family activities were chosen to be of interest to the majority of us--which meant my brothers and not me.
I started college with no knowledge of how to style my hair or put on makeup or dress in anything other than jeans. But I knew all the rules to all the sports, and how to fight (because when all your brothers start taking karate lessons, you take them too, out of self defense), and how to use tools and how to fix things. Going to a women's college was an eye-opening experience.
So I agree, there can be a tendency to a certain type of behavior in a family.
After we were all grown up, I got a phone call from one of my brothers. He'd just found out that his first child was going to be a girl. And literally, this is the conversation that followed:
Him: What am I going to do with her?
Me: What do you mean, what are you going to do with her? (I was completely puzzled.)
Him: It's a girl! I don't know what to do with a girl!
Me: Love her?
Him: But I can't take her out in the yard and shoot hoops with her or teach her to dribble a soccer ball!
Me: Why not?
Him: [long silence]