Leaving aside the discussion as to which approach would be the best for Bitcoin in the long run, we can agree that there is a disagreement on the issue and any hard fork that may happen will not be as unanimous as the previous forks were. Looking at some recent examples, we can expect that any contentious Bitcoin fork will create a split in the network.
Big players can trump forks - Elacoin
Last year Steve Sokolowski shared his thoughts on a Bitcoin hard fork proposal in a forum post. Other than discussing the actual solution, Steve also shared a story of Elacoin's attempted hard fork. Apparently, it was some unremarkable Proof of Work altcoin which activity has died off after awhile. A new developer came in and decided to breathe new life into the coin by creating a Proof-of-Stake fork. A lot of people got excited for the update and the trading volume and price rose back up.
When the fork was scheduled to take place, despite the backing of the community, the developers and stakers, the fork failed since Cryptsy continued to trade the coin without upgrading their daemon. Eventually the hard fork was deemed a failure while the old coins were still being traded.
This brings to mind the famous experiments with five monkeys, a ladder and a banana. People would trade a coin in anticipation of the fork, then ignore the fork and continue trading the coin due to its increased price and volume, completely forgetting why they were trading it in the first place. Classical altcoin speculators.
This only goes to show that big players, even if they are in a minority, can trump developer forks. While a story like this is rather unlikely to happen in Bitcoin, since the coin itself has many different markets and a vast community, we could experience a different problem when a hard fork happens...
New Coke vs Coke Classic - Ethereum
Not so long ago, Ethereum has experienced The DAO debacle, wherein a large quantity of ethers were drained from a high-profile smart contract. This prompted the Ethereum developers to create a hard fork that invalidated the attack. For a few days everything seemed to go smoothly - the majority of the network supported the fork, everyone transitioned just fine and it looked like the network could put the kerfuffle behind them. Then came Ethereum Classic...
Ethereum Classic is, I suppose, an "un-fork" of Ethereum - a codebase designed to ignore the DAO hard fork and continue the network as if it never happened. Whether the developers believe that they are supporting the community that disagrees with the fork, or they just want to make a quick buck, the fact is that the classic ethers (ETC) started being traded on Poloniex, probably one of the biggest altcoin exchanges currently, and now are being actively traded on a number of other exchanges with a current market cap of $200M and 24h trade volume of $65k - forth market cap after Bitcoin, Ethereum and Ripple, and having double the trading volume of Ethereum, second only to Bitcoin...
From a perspective of any Bitcoin core developer wanting to fork Bitcoin, this is probably the worst thing that could have happened in the given situation. Exchanges supporting both sides of a fork can set a precedent of what will happen when Bitcoin is forked in any fashion short of full unanimity. Even if the unforked version of Bitcoin has 1% of its market cap, that's $94M market waiting for an exchange to take their money - it would be the 7th largest coin market, around the halfway point between Litecoin and Dash.
As an Ethereum Developer pointed out in an Ethereum Foundation Skype Chat leak - ignoring Ethereum Classic means there is no money to be made, while embracing it allows you to tap into some "vestigial value remaining from the shared chain history".
Even if any potential fork has all of the support from all of the developers and miners, there isn't much one can do to stop the un-fork, perhaps short of a Coiledcoin-esque 51% attack. Even if networks like Ethereum implemented "the bomb" (a special smart contract that prints tokens out of thin air, intended to kill an un-forked network), a developer could just create another hard fork to disable that code pretty much like the DAO was disabled...
Kill it with fire
So when all is said and done, it looks like the only way to ensure only one version of Bitcoin is around, one would need to reach an overwhelming consensus with the developers, the miners and the exchanges to support only one part of the fork. Anything short of that will create a split network with duplicate tokens being created on both tines of the fork.
To ensure the rest of the network follows suit, someone should put aside some funds and mining power to be able to execute 51% attacks on any un-fork that would start being traded at an exchange. While a 51% attack in normal cases might be in the legal murky territory, perhaps using it to enforce a hard fork might not be seen as an attack on the currency, but as a part of the upgrade process. The law might not catch up to this conundrum for years still.
Anything short of an unanimous hard fork to Bitcoin will most likely result in a network split where both sides of the fork. The split will most likely be motivated by short-term profit to extract some remaining value from the alt-chain. A good way to ensure no such split happens would be to divert some resources to performing 51% attacks on the minority chain and thus causing whatever exchange that tries to trade them to lose money.