I'm a scout leader and we've used the local guiding site many times for camps and activities. We're going later this term to do climbing. We will be gutted to see it close.
I know nothing about badges for guides but Scouts do have a skills badge that involves learning to iron, use a washing machine, sew etc. So it's not all fires and knives!
I never wanted to join brownies when I was a young girl as I didn't want to do the sewing, cleaning cooking things. I'm guessing I heard other girls in my class talk about what they did! I wanted to join scouts, but no girls allowed. I didn't know venture scouts allowed girls, and had probably gone off the idea by then.
I know locally there was a trans girl that joined rainbows, I have no idea whether the child is still there, or whether the other parents were told a boy had joined.