Completely agree with this.
@TooMuchToDoTooLittleInclination is absolutely right. Values ARE always big things. That’s why you have this faint itchy feeling that this phrase isn’t right, @WhatIsThisMad - this phrase is often taking a single conversation or a single topic, and making a broad statement about another person’s values. There was a poster who stated that they disagreed with their brother’s values and he’s a drug dealer and he has other accompanying selfish behaviors - THAT is the kind of situation in which to use a statement like this, when you’ve known someone personally and deeply for years, you truly know their values, and you know yours don’t align. And even then, you might know a drug dealer who has other values that DO still align with yours. But not over a single classroom discussion, or a work colleague, like your intern judging you (he didn’t know you personally, and truthfully, doesn’t even know you professionally, as you are constrained by limits of your profession, your institution, the internship itself - it would have been a bit funnier if you WERE also a staunch socialist like him, OP, but forbidden to discuss personal politics with interns, so he wasn’t to know - I’ve had professors who were forbidden from discussing personal political beliefs in the US).
You can literally agree to disagree and move on - it means you still respect each other, and you’re willing to continue communicating on the whole, because you value the communication more than just that one issue.
But your apprentice saying, “We obviously have different values and that’s okay.” Erm, I didn’t know I needed to be informed that it was okay if my values differed from someone else’s? Because it really is an incredibly pompous thing to say - “your worldview doesn’t align with mine, but I suppose it’s acceptable.” I would have told him that he might have personal values but if he wants to work with a wide range of people, he better work on not condescending to others with statements like that. If he wants to go to work with only people who have the exact same values as he does, then I suppose he’s fine and it doesn’t need any improvement.