I couldn't agree with @Dazedandconfusedpart2 more.
The OPs son is perfectly happy wearing what he does. He’s not getting bullied at school. He knows that ( sadly ) he needs to conform to other people’s expectations outside of his home and accepts this. His sister is happy because she gives him clothes.
There’s no problem here as far as I can can see, except in your head OP.
I say this Kindly and not accusingly. You have decided that certain clothes (and toys I assume ) are “ girly”. However your issue will go away if you stop labelling the clothes and toys.
So rather than saying
“ My son likes girly toys like prams and toy kitchens and Dressing up as a doctor so there’s something wrong with him” just say
“My son likes playing with children’s toys “.
That normal, that’s what toys are for.
When my children were younger I would pretty much let them wear what they liked. So if Jane came back from nursery in her favourite red t shirt with a tractor picture on it saying “ Emma says this is a boys t shirt” , I’d make a big thing of saying
“ Oh no, let me check, has it got a hole for a penis in it? Is there a label that says ‘ only to be worn by boys”? Oh my, the label says ‘ aged 4-5’ there’s nothing about boys ! Has the queen passed a law that says only boys can wear red ? Are girls allowed to be farmers or mechanical engineers?”
Of course this made them laugh. But it’s the very important point that clothes and toys are for alll children. The same as clothes jobs hobbies and music are for all adults. I hate loathe and detest the new unofficial rule in our culture that eg if you Want to work in IT or fancy girls or don’t want to wear make up and hair extensions you must be a man. Or want to be a nurse and paint your nails then you must be a woman. It’s all bollocks.
When my children were small and we went into shops and the clothes and toys were sections labelled with boys and girls we would laugh at the absurdity of it. I’d say “ ok let’s buy a toy for (newborn baby ) James from the girls section and see if the police arrest us on the way out “.
If the lunchtime helper at school was a man, I’d say in mock concern
“ Oh no, how can he do that! Serving food is too hard for men, how will he learn to do the cooking. “ To make them laugh and say “ don’t be silly, boys can do any job “.
I’d tell them that they were probably damaged for life because I used the same red and blue pram for then all and didn’t get a pale pink one for the girls and pale blue for the boys. They are not stupid - they can see it’s about consumerism and persuading people to buy more.
When they were older I talked to them about all theses restrictive rules and who they benefit and penalise. About the status and financial rewards that come with different jobs and roles in life and who gets these.
I hate this modern gender ideology . Honestly it’s like bloody 1950 again.
It’s all damaging and very wrong and I won’t bring up my children to follow this belief system . I want them to be free to choose any job, hobby or clothes they like and not have half of the choices closed off to them because of other people’s prejudices .
My kids are all teens and 20s now. They are all happy in their own skin and their own sexual orientation ( the ones who have decided so far ! ). Some are GNC and some GC, they are all lovely.