DS does boys-only activities (team sport) and mixed activities (Scouts, music).
DD does girls-only activities (dance) and mixed activities (Cubs, music).
They are at a mixed school. DS essentially ignores all the girls, DD tolerates the boys. At home or on holiday we do a mixture of things without any thought as to whether they are traditionally male or female - canoeing, maths, going to the theatre, playing with lego, gardening, cooking, reading, playing board games, trampolining, making animated films, hiking, body-boarding, visiting castles.
Neither child regards any part of life or any activity as being 'closed' to them by virtue of their gender. They know that some of the things that they enjoy doing are done mostly by girls, or mostly by boys, but they do not choose those activities because of that, they choose them because they like them and enjoy them and are good at them.
I find the whole discussion quite odd, actually.