The trouble with this is you are missing a huge point here.
DS is ten. He has no interest whatsoever in girls. But then he has no interest whatsoever in boys who play football either.
We had a conversation with him about this not long ago. There is a girl he does talk to and seems to get along with at an out of school activity he does. His comment was that he didn't have anything in common with the girls in his class. He regards them as somewhat vacuous and only into beauty stuff and Taylor Swift. But that's not a lot different to the boys who are into football. He said this girl at this activity was "the only girl who he has something in common with". He doesn't have a lot of time for the boys who actively look down on him because he doesn't conform and fit into their gang. He took exception to a teacher describing his classmates as his friends. He commented "just because they are in my class, doesn't mean I'm friends with them. I just have to get on with them but that doesn't make us friends".
And actually that's a fairly mature understanding of the difference between acquaintances and colleagues and actual friends you seek out, want to spend quality time with and trust.
And the problem lies with the 'enforcement' and the bullying that comes with non conformity. The 'in boys' other the children who aren't in their gang and are part of their collective identity. This is where gender stereotypes and obligations to follow them matter and are problematic. Not a disinterest in another child in the class. It's about forced interests and the closing off exploration of interests because they are 'girls/boys' interests.
It's about the formation of hierarchies within society at an early age. And how they are propped up and enabled by adults. It's tribalism that's ultimately the problem here. Boys who like Taylor Swift are quickly made to be embarrassed and told they are effeminate. Likewise girls who like football are quickly told they aren't good enough, even if they are more skilled.
Disinterest, in its self isn't a problem. As adults we all have people who you really don't particularly want to engage with and pretend to be best buds with. And that's ok.
Your argument here neglects the point that girls do the same thing in terms of general disinterest. They don't want to engage with the boys for similar reasons.
There's one boy in my son's class who has been somewhat rejected by the other boys (he gets on with my son well but he doesn't fit in with the rest of the group). He's one of the most immature, smallest and struggles with gaming because of motor skills issues so doesn't have that in common. The result is he's ended up playing with the girls who he does get on with, but he still wants to play with the boys. Put him in a different environment with some of the same boys (including DS) and they get on amazingly well. The issue is the social space and hierarchies which don't allow you to get to know peers in different ways and to find common ground in different ways.
The issue here is these same social hierarchies exists across the world - they've studied it in numerous different cultures - and there's these same patterns of the sporty ones and the cool ones having higher society status than the outsiders and nerds.
This is where how you teach tolerance or authoritarian ideas matters. If you have a society that places higher value on enforcement of conformity. This is where sexism starts to fit in. It's about conformity and non conformity.
Perversely if you go too full on with enforcement of 'inclusion' you stray into the realms of authoritarianism of forcing kids who don't things in common and genuinely don't get on, see how quickly they kick back and complain because they want to play with their mates. You can't force the issue. You can only gently put kids into different scenarios with new experiences away from the set social bonds and change attitudes.
So putting the all football kids with the girls who like Taylor Swift and asking them to get on won't work. Put one with another and a whole group of different kids doing a climbing activity they've never done before and you might get a totally different response. Because you have a reset and are on neutral ground.
The kids start to mix when they are older because they suddenly have something in common - hormones! And that's a natural reset point.
You can make that work if you then have healthy peers and influences about how you treat the other. That's doomed from the off if your only reference points are unhealthy online echo chambers and porn. That's why the whole role model thing is relevant.
But equally the macho attitudes of parents does impact here. Football and a somewhat toxic masculinity go hand in hand in a way that's different to other sports (each sport has its own culture surrounding it). Why does football have hooliganism when other very masculine sports don't? That's the type of question you should ask...
...the answer comes back to tribalism and power every single time.