I say just stop being such a massive fanny about it.
Do the shoes come off before crossing the threshold?
Are they then inserted into hazmat bags before coming into the house? (Done wearing disposable rubber gloves?)
Then the whole process in reverse before leaving the house?
Yeah I get it. Shoes carry germs. Guess what? So does EVERYTHING else.
Stitchy if I squared up like that in kumite practice Hanshi would whack me across the legs with his shinai. See how you're leaning back and your weight is off your front foot? One kick to your front knee, which is unprotected, would hyperextend your knee joint, you'd go down like a sack of shit and you'd probably walk with a limp for the rest of your life.
Domo arigato gosai mashita! OS!