If you don't live in the UK it's not your community being discussed here, so why are you getting involved? If you don't want "white privileged women" getting involved because it's not our community, why are you doing so? It's a bit hypocritical, no? British women are a community.
Unless, of course, you think British Muslim women have more in common with eg Indonesian or Qatari muslim women than with other British women. But then that's you "othering" British Muslim women, no one else.
I understand the religious reasons for separating men and women for things. My religion does similar. What I don't understand is a family fun run where there's no participation allowed for women or female children aged 12 and over. If this were my religious community arranging this event I would complain about it too. It should be up to the individual women to choose not to participate in a family day if they feel it's not in accordance with their religion, they shouldn't be told they're not welcome to.
As it was framed as a family event there should have been separate events for men, women and children, or even just for men and women and children could join whichever race their parents were in.