What, if anything, can I do with the "progessive" man in the Lansdowne Residence?

This guy is just there for flavor, and I believe he's referring to the fact that he's "for" the Vox Populi. He's a civilian, and as I've noted previously you can murder civilians with impunity, although they are very unlikely to give you any loot.

Later there is another residence you can pass through with more of these progressives, who appear to be harboring some wounded workers or Vox members. There's a tutorial popup about "violence" perhaps not being the only answer here. If you spare these folks, they'll send away a police patrol that knocks on their door after a few seconds. Otherwise, the police will burst in when they hear shooting or when nobody responds.

However, the police patrol hangs out outside, and you'll have to fight them eventually. The overall choice here is relatively minor.

pro·gres·sive
A person advocating or implementing social reform or new, liberal ideas.

People view you as the false shepard, the man here to destroy their way of life. When someone says they're a 'progressive,' that just means they support you.

There is nothing special you do with them, they're just there to add to the atmosphere.