I don't know if the rules mention that you need to wear your pants on public transport?I am literally riding the southwest chief barefoot as I write this. I was told to put footwear on because there is a chance my toes could be cut off between the cars. However, the FTA does not require footwear to be worn by passengers on public transportation.
Feel free to enjoy your barefoot visits to those Amtrak bathrooms... Yeuk!
The thing is that many passengers are first time riders, and most folk "expect" the floor to be solid, not to move under their feet. They are unprepared for the swivel action of the cars causing the floor to pinch together between cars.
Sitting in your seat without shoes is fine, but put them on to move about the train... Your travels might become more "footloose" than expected otherwise.