Bacara never taking off his bucket because the HUD will accurately list all emotions other sentients display openly towards him he can't identify by himself.
Fox never taking off his bucket because the visor will safely hide all the emotions unidentifiable in his pleasant voice and rigid posture still raging in his eyes.
Both strangely feel safe when forced to take off their buckets in each other's company, maybe due to some kind of problem with the reg filters. They never talk about it so they never pinpoint why they trust each other explicitly.