I come from a very rough and tumble family and I don't think either my mum or I, have a tendency to treat babies differently based on their sex. We are extremely affectionate to baby boys and girls, while also being quick to throw and swing them through the air as soon as their necks are strong enough. While encouraging them to be active and mobile as soon as possible, whether a boy or a girl. I think it comes from the fact that both my DM and I were considered tomboys as children. We are both grew up feeling stifled by other people's perceptions of us due to our sex and have a pretty strong drive to make sure baby girls in our care, get to have every bit as much fun as baby boys. While we're also on the more daring end of what we'll encourage babies to do.
In an interesting twist though, my DM is insistent that my DN is wilder and more physical than my DS was, because my DB, DN's dad, was wilder and more physical than I was. She thinks DS is just like I was and DN is just like DB was. My DS surpassed physical milestones at a very young age, ie attempting steps at 7 months, controlled walking before 10 months, cycling at 3. But my DM insists that if DN had been encouraged like my DS was, she'd have been even faster.
And while my DB has always been consistently sporty, I do think a lot of that has to do with him having a lot more access to sports as a child. I was always underestimated in sports because I'm small, which would have been fine if the coaches would let me play, but they used to put me on the younger teams, which I hated. Especially as I was actually good and would almost always score or defend well, if i was given the chance. While the sports that I am best at, that I was always drawn to as a child and have turned out to be really, really good at as an adult, were too expensive for my family when we were kids.