Funny how feminist now is supposed to mean including men or boys, as if girls or women are letting men and boys down if we don't include them, or as if a group of girls or women is deficient if males are not included.
"I would be frankly ashamed if my child only had friends of one gender"
Presumably your child is quite young still?
They are free to choose their friends in my family and can use any criteria they want when choosing, and I am not ashamed of any of their choices or their criteria.
DD1 chose nerdy girls from the hippie fringe of her class from age 5 to 13. About age 13 she turned into the queen of prep, and she and her friends went to different secondary schools. She became friends with a girl from her primary school whom she had never had much in common with up to then and they are BFFs now (aged 26). DD2 chose nerdy girls from very devout Catholic families of German heritage from age 5 to 13. They are all still friends though their circle has widened considerably and includes many boys 
(men now since they are 20). DD3 chose a wide variety of girls from age 5 to 13 though she had one close friend from whom she has drifted apart in secondary as they were never in class together or at the same lunch. Weirdly, most of her current friends are dedicated dancers though she herself has never danced apart from two years doing Irish dancing. DD4 chose a wide variety of girls who had in common the fact that they were all only children. I wondered what she was trying to tell me, as she is the youngest of five.
The DDs all enjoyed their friendships, their fights (in hindsight), the sharing of interests, being in girl scouts, being on girls' sports teams. They learned lots from spending time with other families, and had a good time with their friends at home too.
DS had different groups of friends in primary, all boys. He felt a bit intimidated by the girls in his class, all very kickass, bright, outgoing girls. There was a group of (boy) jocks that he hung around with for a while but drifted out of. He didn't enjoy being mashed into the ground during an afternoon of football. The boys all knocked together well in secondary, which was the time when DS settled into one particular group of boys, all of whose members he had known in primary school. They are all still friends even now after university when they went their separate ways, and spend a lot of time together, though the circle widened to include girls long before they all went off to university. Their interests as teenagers included Lord of the Rings, nerf darts, sports, sports, sports, sports, sports, basketball, football, baseball, football, hockey, hockey, hockey, hockey. (Did I mention sports? Did I mention hockey?). DS as an individual added cavalry and artillery of WW2 to the previously stated interests in his teen years.
Should I have forced DS to take an interested in clothes shopping? Should I have forced him to be as interested in art as DD1 was? Should I have forced DD1 to become familiar with the marvel of engineering known as the T-34 tank? Should I have forced DD4 to be as interested in art as DD1 was? Should I have forced DD1 to ditch the preppy outfits and dress like DD2 in neon t-shirts and sport shorts and sweatpants?
There were girls in their classes and on teams with whom the DDs never clicked, and girls who were pretty much soulmates. DS for his part gravitated to boys who were interested in highly technical details of whatever they were doing. There were boys who were very different from him and personality-wise they had little in common and they did not spend time together. It's a bit ridiculous to suggest this is a case of all girls being friends together vs. all boys being friends together. There is a lot of discrimination within sex segregated groups.