Last Friday morning I woke up to my nine-year-old son shouting: “Did you see that Lucy Bronze goal!?” as he burst into the bedroom. His six-year-old brother was right behind him, earnestly re-enacting the England player’s 20-yard thunderbolt with all his might. They’d followed our usual protocol for evening kickoffs on school nights, inaugurated with England’s men in the World Cup last summer and honed with Liverpool in the Champions League this season. They watch the first half with my husband and me before bed, then watch the second half on catch-up the next morning.

That this time it was women playing rather than men made no discernible difference to their levels of interest or excitement. For them it was just football – and compelling football at that, in which England were doing well.

A friend's club now runs girls’ teams for ages five to 14. It has even inspired some of the mums to start a women’s team

Four years ago, when the Lionesses reached a World Cup semi-final, I tried to imagine how much that would have meant to me as a football-loving girl growing up in the 1980s, when women weren’t welcome in the sport. But in many ways, this feels like a bigger shift.

And I’m not even sure the impetus came from us. While raising feminist sons feels like one of our more critical ambitions as parents, we tend to do it in an ambient, equality-as-background-wallpaper kind of way. We haven’t force-fed them women’s football at all. Yet they’re still really into it.

I first noticed when a poster of the England forward Toni Duggan appeared in a coveted spot alongside those of Lionel Messi and Trent Alexander-Arnold on my sons’ bedroom wall. It had come with the BBC’s Match of the Day Magazine, whose efforts at normalising women in football should be applauded. My kids didn’t see a photo of a woman, they saw an English footballer in a Barcelona kit.

Lucy Bronze, the England player who won me over to the World Cup | Rebecca Nicholson Read more

I’m sure it also helps that one of the best defenders in my eldest son’s side is a girl. Nicknamed “the warrior”, she times her tackles perfectly, is strong on the ball and even throws in the odd audacious Cruyff turn when she’s bringing the ball up the pitch, much to the delight of her coaches and all the parents on the sideline. One of the best players in their league is also a girl, a deep-lying playmaker with rare composure on the ball.

In the playground, things are evolving. My eldest son tells me two girls in his class now play football with the boys at lunch rather than just on their weekly designated girls’ football slot. Which definitely didn’t happen when he started school, but no one bats an eyelid now.

All around, all-girl teams are flourishing. A friend who coaches his daughter’s under-eights team tells me there’s been an explosion of interest in the club over the past four years. They now run girls’ teams for ages five to 14, and it has even inspired some of the mums to start a local women’s team.

My hairdresser used to despair at how bad her daughter’s all-girl under-sixes team was compared with her sons’ sides at the same age. But her daughter and the team stuck at it and they’re now in a mixed league, frequently beating all-boy teams. She describes their reading of the game and positional play as way ahead of what you’d expect for players their age.

What I’ve found most refreshing about watching this Women’s World Cup with my sons is that they’ve not once compared the quality of the men’s and women’s games – a tedious discussion that never seems to happen in other sports such as athletics or swimming. The battle of the sexes is just not on their radar. The only difference between the genders that has been remarked upon was when my younger son asked why the women spend so much less time than the men lying injured on the floor.

Kids are interested in goals, skills, stories and celebrations. Unsurprisingly, Megan Rapinoe of the USA has become a quick favourite. They love Stina Blackstenius from Sweden too, for her goals and no doubt her name, which feels like it’s been lifted straight out of a storybook. But tonight all eyes will be on the Lionesses and, as was the case when the men played Croatia last summer, because it’s England in a semi-final they’ll get to stay up for the whole game.

The main hope with England’s World Cup run is that it will inspire more girls to take up the sport; but the fact it’s helping boys and men see women playing football as normal feels incredibly important too. It was great to see David Beckham at England’s quarter-final against Norway last week with his football-loving daughter Harper (though I couldn’t help feeling the symbolism would have been even more awesome if his sons had been there too).

There are of course still plenty of people debating whether the Women’s World Cup is worth watching, despite the record-breaking BBC viewing figures. I’ve heard the odd comment – usually from older men who just can’t get into it, that they are “really enjoying the cricket”. Happily my dad is not among them. In April, when I asked if he was watching the football that night – meaning Liverpool v Porto in the Champions League – he said, “I have it on now, England v Spain.” He meant the women’s team.

And for a new generation, the rejectionist mindset seems as curious as the very idea of women playing football did when I was growing up. And I’m very thankful for that.

• Sam Haddad writes for Guardian Travel and the Guardian Bike Blog, and is senior editor at Mpora