The Red Sox helmets are that way largely because of the amount of pine tar the team uses and the ability of that stuff to get on everything and everywhere. It is largely hidden on Navy Blue but the logo area on top does look disgusting on most of the helmets.
They are usually dirty from sliding or the pine tar from their bats. When they go up to bat they put pine tar onto the bat for grip, then they might touch their helmet accidently, getting the pine tar onto their helmet.