Egg color has to do with breed and diet, the dominant hen type in the US produces white eggs but brown are fairly common. At the co-op I can get eggs that are blue and green, just different breed of hen. Washing does not affect color in the slightest.

I'm guessing that a co-op wouldn't use the same industrial corrosive washing that larger agri-corps do; it'd be a lot closer to how the rest of the world washes their eggs.

I would presume "co-op" here is a market, not a farm. The co-op near where I live is one if not the oldest example and is part of a giant network of co-ops... they certainly don't wash their own eggs: they source them from distributors much like any other market, and it isn't even inherent to the premise that they are using local sources (though mine does care a bit more, as it is a natural foods co-op, the goal of being a co-op is mostly about having a fair and equitable ownership model of the company that enables both employees and customers to have equity).