Getting dirty outdoors is good for children, and most of the worry about it is out of proportion to the actual risk. The goal is sensible hygiene, not a sterile childhood.
The moments that genuinely matter are before eating and after using a toilet. Those two habits do most of the work, and everything else is a distant second.
Keeping wipes and a hygiene kit in your bag means you can say yes far more often. Most refusals to let a child do something messy are really about not having a way to clean up afterwards.
Teaching children to handle it themselves is worth the slower start. A five year old who can manage their own hands and their own mess is a five year old who can be trusted a little further away from you.