We have 3 children and no pets. I must admit that nobody wears shoes into the bathrooms here...as they only go in there to have a shower in the morning, so we all have bare feet.
And during the day we don't wear shoes around the house, only put them on before going out.
We have 3 bathrooms, the first one is quite small, the second one is an ensuite, the third is the biggest but is more of a guest bathroom that we only use ourselves when we are in the downstairs area...but we don't shower in there.
Actually I think our bathrooms don't show dirt much because they all have really horrid old tiles from the 70's, in very busy patterns, so the dirt really doesn't show, lucky for me!
Also I put bathmats down which get changed often, and I also vacuum weekly, and mop every 2nd week.
I guess when I get my wish of renovated bathrooms, the floors may show dirt more easily...