If it’s wet or snowy out, I throw down a town on my way out, so my dog has no choice but to step on a towel on the way in. Combine that with using a leash and she has no choice but to stop until I’m satisfied with her feet
My sister-in-law does similar with a bucket of clean water, so she even gets dry dirt off, but that’s excessive.
Humans have lived in filth their entire existence and whatever being tracked in, if it’s not visible, it’s cleaner than most of human history and it’s clean enough to not cause harm