How do you justify the against their will part with your earlier sentiment that you don't understand why people care if its biology or cultural.
If its biological, forcing them outside of their biological comfort zone seems particularly cruel.
In adults, it's different. They should be offered the option and decide for themselves. It is still good thing to do from time to time.
In any case, you need to be sensible as a parent. You shouldn't push children out of their "biological" comfort zone. For example, if a kid is afraid of spiders it is not sensible to push him to have one as a pet. It might be sensible to go to a zoo to see one (among other interesting animals), though.
Gender-based biological differences are subtle enough to not really matter in a summer camp scenario.
I am not really sure I buy into "treating boys and girls the same" either. I think what's more important is to give them options (perhaps against their will, to get them outside the comfort zone).
It seems to me that schools already largely do treat everybody the same, even to the point where it is being truly annoying to open-minded individuals. I am not sure it's ideal to treat all kids the same, but rather recognize their individual differences.
For example, my parents sent me to summer camps to learn some outdoor skills. I wasn't very good at it and I didn't enjoyed it as much as I probably should as a stereotypical male. But on the other hand, I think it was right thing to do.
So, if despite these attempts to make me into an expert in wilderness survival, I didn't become one, and rather became computer geek, which was certainly out of fashion at the time, I have serious doubts about the theories that cultural ideas are so influential to the actual behavior of children.