To first century Jews, cleanliness was a big deal, with practical reasons blended with religious beliefs.
There were detailed instructions for how priests were to prepare themselves and vessels for temple use. There were then those—the Pharisees—who wanted to make those same ritual washing laws applicable to common life. The bottom life being that outward cleanliness was to be a marker of inward cleanliness.
Then there were those suffering from leprosy, who would have to announce their passage down the street by shouting, “Unclean!” just like we might honk a car horn or ding the bell on our bicycle today. For them (and not for bad reason, lest they infect others), their uncleanness kept them separate from society. For many, of course, such an outward disease was also an indication that there also must be some sort of spiritual disease (sin) as well. Which is also why, upon being cured, a former leper would have to get the approval of a local priest, who also had the authority to pronounce them sinless and forgiven.
Then there’s the remarkable behavior of Jesus, who didn’t seem as deterred by uncleanness as others were. Whether that was those suffering from obvious external uncleanness (like the lepers), or more hidden internal uncleanness (like Judas). It’s as if his motto was a countercultural, “Keep the clean close, and the unclean closer.”