Yesterday, I wrote about bad PC behavior and why NPCs generally seem to know about it going in.
Should that be a point-costed Reputation in GURPS?
Briefly, Maybe, but I run it as No.
In general, I don't assign a point-costed Reputation for such behavior, unless it's explicitly personal behavior by a specific PC. General behavior by a whole class of adventurers gets covered by the usual steep reaction penalties that delvers in a dungeon-bashing game get - penalties for invading the living space of the encountered NPCs, penalties for cultural divides and language issues, penalties for perceived and actual prior behavior. Negotiation is still possible, but if you murder-hobo as a main approach, you are putting yourself at a disadvantage. NPCs might take a risk on you, but only if they have to, or you make it so tempting to do so that they overcome their risk-aversion due to reward-greed.
In town, NPCs react off of the PC's disadvantages. They're sufficiently two-dimensional that I don't worry overly about giving them specific problems with PCs. The PCs can create those issues themselves, but if they don't, they don't exist beyond that which they gained points for.
So while being a standard PC and acting like a standard PC - killing for loot, taking no prisoners, and sparing no pity - gives a blanket problem, you don't get points for it. It's just a campaign switch if everyone does that all of the time.
If you take a nicer approach, though, you can negate that. It takes a bit of effort - and it's worth buying positive reaction traits to overcome the automatic assumption you're a murder hobo like the rest. But consistent behavior the other direction can change that campaign switch of expect all delvers to be untrustworthy murder-hobos. You just have to put the work in to prove it. If you do, though, it's possible to reap the rewards of being nice. However, a little trust-breaking can undo a lot of trust-building, so the work needs to be consistent, as well.
In all of these cases, it's possible to grant a blanket Reputation to all delvers . . . but it'll be earned through play, and serves only to reduce the effective value of a PC. Since my game uses a flat cap on the maximum negative points on a PC, this really doesn't help very much. It just adds the complexity of putting down disadvantages on paper without getting any real game utility out it. So I save Reputation for individuals and what is known about their actions individually.