This answer is specific to burning-wheel.
Burning Wheel Gold, page 104
Basic, Naked Characters
Characters start the game naked and stupid. Literacy is earned through skills. Clothing is purchased with resource points.
Burning Wheel does not coddle the players. If they want something, they need to work at it. They'll fail along the way, but those failures will spur interesting and unexpected developments. Getting expensive things is hard!
They shouldn't have a creative story as to how they got their shield, unless in character burning they bought the shield with resource points or they acquired the Family Heirloom trait (page 325).
If they want to make a shield, they should get the raw materials (Resources, perhaps Mining), find an armorer (Circles) and convince them (Duel of Wits, Haggling, Resources) to use their workshop (unless they bought one with resource points), and test their Armorer skill (not Blacksmithing).
If they want to buy it, it looks like an Ob 3+ Resources test depending on how fancy it is; get some friends to help or find someone to give them a loan. Or they can go adventuring and use the resulting treasure as Cash on Hand (page 374) dice to buy the shield. If they fail the Resources test, you can invoke the Gift of Kindness (page 370). If they covet someone else's shield, they can go steal or fight for it.
In my first Burning Wheel game, my character started without shoes, and it sure as hell caused some problems.
If getting this shield is important, they should write a belief about it. You should challenge that belief against their other beliefs. How badly do they want it? Find out in play. This isn't GM fiat. This is using and engaging the rules of the game. Depending on what other games they've played, they might not be used to it.
First, set up a Conflict Web. Start by setting up your factions that are involved, and why they are competing/conflicting. This is more to give you a set of motivations for any given group, leaders, etc. and allow you to simply improvise based on the group's needs/ambitions.
The Conflict Web is not static, it's a starting point. So you may easily see characters shift alliances or make temporary truces to accomplish goals.
Second, once you situate the PCs into the scenario, look at their goals, and likely problems they will face in terms of Logistics and Politics. This is effectively similar to how Apocalypse World produces "Fronts".
After each session, look at what the PCs attempted, who was affected, whether any NPC groups made major moves and figure out who is going to react and how. You can choose to update either the Conflict Web or the Logistics & Politics list, though I usually find myself only having to do serious updates after 3-6 sessions because it's relatively easy to track what happened with simple notes.
Both of these tools can scale up or down, so you can do intergalactic empire politics or the 28 guys stuck in a prison together, based on whatever fits your campaign.
Best Answer
As others have mentioned, this is a play-style issue that needs to be worked out amongst the group to avoid hard feelings, misunderstandings, and frustration. However, if despite prior discussions/agreements you find you're about to face conflicting character reactions, there are steps the GM can take to reduce players ability to dominate such scenes and pre-empt other players actions.
Give reacting characters a chance to intervene. When the characters are in a tense situation, and a player decides to take an action that would eliminate everyone else's choices, such as starting a fight, giving up a contested item or NPC, etc., allow the other players the opportunity to react first to that action. Keep the resolution of that action within the group. While other players may not get to do exactly what they planned from the beginning of the encounter, they will still be in control and using their actions to determine how the event plays out. When hostiles are confronting the PCs and the PCs start to fight or argue amongst themselves, it's not unreasonable from a plot perspective that other groups won't interfere, at least not immediately, until they see which way the conflict is going. So it's usually going to be believable that the PCs will have a few actions to resolve their differences before the opponents interject themselves.
Example:
Player 1: "I'm tired of this prattling. These guys are gonna get what they deserve. I attack the leader."
GM: "OK, hold off on your attack roll for a second. He looks like he's going to attack. How do you react?"
Player 2: "I grab his sword arm and try to talk him down."
Note: This is really a mitigation technique for your GM toolbox, for times when you don't have a firm social contract to fall back on. Also, keep in mind this is predicated on having mature players who can deal with interparty conflict and still keep things civil at the game table.