It's surprising because in an emergency where EMT is called, if I found out they stopped outside my door to remove their shoes, that they would then have to put back on before we can leave, I would be a little pissed.

I honestly do not care at that point if you jumped in a mud puddle and are tracking it through the house, it will get cleaned up when the emergency is over and nobody's life could be in danger.

Let's say I call emergency services because my spouse is having a seizure. If emts stop to take off shoes instead of come in, put them on a stretcher, and leave, they are wasting time in my opinion. Time that my spouse may not have. I don't care if it's 3 seconds TOTAL. That's 3 seconds that could have made a difference.