The white-coats are behavioral scientists who oversee Alex's treatment as he undergoes the Ludovico Technique. Both are soulless and content with their work. They're not exactly personable, and are more than a bit patronizing to Alex:
"You had a very positive response. Tomorrow, of course, there'll be two sessions, morning and afternoon, and I should imagine that you'll be feeling a bit limp at the end of the day. But we have to be hard on you, you have to be cured." (2.5.5)
They don't understand Alex (nor do they have any interest in doing so) and they aren't bothered one bit by Alex's inability to make moral choices. In fewer words, they may well be the soulless automatons (or "clockwork oranges") that Burgess opposes so vehemently.