Though I don't claim to be a Bible Scholar, it seems that this particular "hygiene law" had reference to setting up camp during a miliary campaign. Deuteronomy 23:10, one of the preceding verses says: "When you are in camp during an expedition against your enemies, you shall keep yourselves from everything offensive." In this context the advice to dig latrines outside the camp during a military operation in enemy territory makes sense, and to cover them up so the enemy doesn't smell the presence of an attacker is also good advice.
Perhaps Essenes had a governing body that took these verses out of context, instructions for mobile military operations, and applied to them a settled community. Kind of like the JW Governing Body that applies Old Testament dietary regulations to forbid modern life-saving medical procedures