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I don't understand the question.
Exactly, I've never washed a pair of running shoes and for half of the year my local parkrun often involves running through sections of 4" deep mud or 6" deep puddles.
I have more than one pair (of both trail and non-trail shoes) in case they haven't dried by the next time I run. Otherwise most of the mud drops off in the first km or so of the next run.
I don't understand the question.