Obviously this is an issue that mostly needs to be fixed by men, but OP, I think you were asking more specifically what can Mums do, so I'll answer from the perspective of a son.
I think the most important thing you can do is let your sons see you as a person, as a human
Growing up, it felt like so many of my friends didn't actually know their mothers. They just saw them as Super mum, someone who just organised everything in the background and made life run smoothly, but they didn't actually know that much about them. They knew Dad's stance on all kinds of stuff, because Dad had time for conversations with them, because he wasn't running around trying to make life run smoothly.
My Mum seemed different. Part of it was that she had cancer when I was 14, so I got to see her scared, and worried, and at times with her dignity in tatters. And I got to see the effects of my Dad's behaviour when he had affairs. I'm not saying she didn't try and keep the worst of it from us, but me and my brother definitely saw her hurt, which I don't know that a lot of boys of my generation ever saw.
But it wasn't just that side, it was the fact that she tried to actually have deep conversations with us. My friends all had shared interests with their Dads. They'd know Dad's opinion on politics, but not their Mum's. My Mum loathed sci fi, but she sat and watched Star Trek with me every week, because it was an opportunity for conversation. When I got a computer, she played the games I bought, because again, it was a way to bond. She did the fantasy football with my brother, because again it was a way to connect.
I think for a lot of boys, Mum is more of a force of nature than a person, and when their primary example of a woman is someone who's feelings you don't have to worry about, it's easier to see all women like this.
I reminded my brother of this a couple of months ago. His son is 9, and he'd just had a really good day out with him, watched the football, and my brother was saying how they'd had this really deep conversation. I asked him when the last time SIL had managed to have a day like that with him and he went very sheepish.