Once you've completed the Blind Betrayal quest by saving Paladin Danse he is exiled from the Brotherhood, but he is still available as a companion. Under these conditions, asking Paladin Danse to accompany you will prompt a warning that while he is travelling with you both of you will be considered enemies of the Brotherhood. Any Brotherhood of Steel members that you come across will be kill-on-sight.
Now, obviously, fast-travelling to the Prydwen and stopping by Maxson's quarters to say hello would cause some real issues. But what about the random-spawned Knights and Vertibirds that you'll encounter in the wasteland?
Are there any long-term ramifications to killing randomly-spawned Brotherhood members while you are with Paladin Danse? Will killing these enemies hurt your relationship with the Brotherhood once you're no longer travelling with Danse?