First answer:
It was on the hard moves list at one point, but I removed it because it wasn't benefiting the fiction. There's a trap hidden inside of "hard move: give someone a Condition," one that takes the story away from the PCs in a not-good way.
Social stigma doesn't just appear. It's the product of specific people being shitty to one another. So, at the very least, the hard move should be "An NPC gives a Condition to a PC." Otherwise, you, as the MC, are reaching into the fiction and dealing out stigma as a player. If we're to uphold the "to do it, do it" principle, then it's important that every Condition stem from a specific character doing/saying a specific thing.
But giving NPCs that power to attach stigma and social value statements to PCs is serious business! And since we're here to be fans of the PCs, and our NPCs are to be treated like stolen cars... having that social power planted in the hands of anyone you choose is going to lead to a situation where the players are navigating your social rules, rather than you reacting to their social power. That's an observation that came out of playtesting. It made the game less Monsterhearts, more Vampire: the Masquerade.
So, the solution: NPCs can spend their Strings to place Conditions. This means that only characters who have emotional leverage over PCs can fuck up their social standing. This keeps the "NPC giving a Condition to a PC" interaction grounded in a PC and their relationships, rather than grounded in an MC's characters and choices.
Second Answer:
That's the design choice I made based on my play experiences. But I also include a chapter of the book where I encourage you to tinker with the game and add new principles/moves/whatever.
So you can definitely add this as a new Hard Move. There are some design decisions that I'd slow-motion-dive to protect, but this design decision isn't super vital (despite how vital I may have just told you it was, in my first answer. I'm melodramatic). Tinker and find out what happens.
I'd strongly recommend that if you do include this new hard move, you word it as "An NPC gives a Condition to a PC." Otherwise it's amorphous and not tethered to character actions.