Yes, and my play expectations are very open-ended and more or less come down to anything goes. I'll argue against restrictions that aren't setting-based, other than a very few clear no-go areas e.g. sexual assault, even if those restrictions aren't going to apply to me: for example if my character idea is a goody-two-shoes knight in shining armour I'll still argue against banning evil PCs.
If that didn't include killing shopkeepers as the way to make their living, then no, the GM is not obligated to support it.
I disagree. When I DM (which I do about half the time) I run the game/setting for the players to play in and, to a large extent, do what they want with. Their characters are their own to play as they please. As such, it's simply part of my job as DM to hit whatever curveballs they throw at me at such times* as they decide to throw them.
As a player, I feel justified in expecting the same of that game's DM.
* - sometimes I'll go years between having to hit a curveball, other times they come fast and furious.
I was responding to the following: "If the players/PCs decide that killing shopkeepers is the way to make their living, in my view it's the DM's job to run with it as part of letting them play their characters as they will."
The above is a GENERAL statement as to the DM's job,. I am noting that the DM's job in this case is not general, but specific, relative to the specific agreement with the players. You may have whatever session zero you like. You, specifically, as a GM, may respond to this behavior as you wish.
On the shopkeeper thing: I think there are features of D&D that can make this a surprisingly acute source of pressure.
D&D emphasises gear as an important aspect of character build. The GP system - including but not limited to starting money - is the mechanical framework for this: GPs are limited, gear has costs, so there is a mini-game of gear optimisation.
But D&D also locates this minigame within a fictional context - the players are supposed to imagine their PCs wandering from shop to shop, pulling GPs out of their pouches and buying the stuff they need, etc.
So it's easy to see why a player might come up with the idea of exploiting the fiction to endrun around the minigame constraints and get the gear by stealing it. And from there it's a pretty short journey to killling shopkeepers.
The problem is only compounded by the fact that there are some aspects of play where trading on the fiction to endrun around the mechanics is considered skilled play (eg circumventing a low STR score and hence a poor ability to open dungeon doors by using tools to break through them or knock out their hinges or whatever; using water or a level or similar to detect sloping passages without regard to the mechnical chance a dwarf or gnome has to detect them; perhaps even using a Rock to Mud spell to bury enemies in a mud-flow without having to ablate all their hit points; etc).
I'm personally not that interested in running a game focused on killing and robbing shopkeepers, but I prefer to get to that end through system modifications rather than session zero admonitions.
Just make the place where the shopkeeper keeps all his good stuff is a highly defended area. Say underground with multiple pathways, traps, and hired monster that patrol the area regularly. Hey wait a minute....