Anyone riding a horse of mine in a saddle will wear the correct footwear. I will let them wear my boots, though. I wouldn't want anyone wearing shoes that wouldn't come right out of a stirrup or that could go right through if there was an accident. Bareback, I wouldn't be so strict. Kids would be required to wear a helmet. Shorts I don't worry about. They can learn themselves why I don't wear them when riding
There is a reason we wear the things we do when riding. Personally, I think it is just as important to make sure someone is dressed properly as it is to make sure and put them on a safe horse.
Just to make it clear, in this post I am talking about those friends that have little or no riding experience. If you have a friend that has lots of experience and is an adult, then I would let them ride in anything they wanted to.