Is it possible after being told to get lost? Each time I return, they are red.

Errr...which faction? Several factions are beyond redemption if you screw up with them in their first few quests to gain their trust. Brotherhood of Steel being the easiest one to screw up that I've encountered. Need more info.

Oh. They are Fiends. Outside patrols blast you but inside, the gate keeper talks to you then turns red after realizing you aren't one of them but doesn't shoot unless you linger for too long.

Try wearing a "Great Khan's" outfit. Leave followers outside.

Unless you pass a speech check the first time in I think they may be hostile to you from now on without the chance of a second try. I'm not a hundred percent on this though...the game is a bit glitchy and your experience may be different than someone elses.