Bitcoin Unlimited is a Bitcoin full node implementation that allows each node to select their own block size limit. The claim and allure is that with Bitcoin Unlimited, you have the power to vote with your full node and with your economic power for what the block size should be. If a node picks a block size that is too small, they will be forked off of the network because they will not be following the longest chain. If a miner picks a block size that is too large, the block will be ignored because not enough full nodes will see it and accept it. The market gets to decide which block size is best, and thus we can resolve the block size debate by leveraging the power of the free market.
As a practical idea, this has a lot of problems with it. When part of the community decides it's time to raise the block size, the miners are the only ones who are able to reliably signal that they are ready for a change, because they are the only entity in the ecosystem that has protection against Sybil attacks. But lets assume that there's some practical way to figure out when the economic majority is ready for a change.
So, now we have to understand what counts as an economic majority. During a contentious fork, you get two chains. In a really bad fork, you might get more than two, and there might not be any clear winner. Ethereum and Ethereum Classic are a great example of what happens during a contentious hardfork. The community splits, and in the case of Ethereum the economic and political majority clearly favored the hardfork, with a economic and political minority preferring Ethereum Classic. Any block size adjustment within Bitcoin Unlimited is likely to have the same outcome.
In Ethereum, the exchanges, the services, the websites, and the developers all followed the hard fork. Individuals tend to trust the developers heavily in the Ethereum ecosystem, and most of the individuals followed the developers during the hardfork. In Bitcoin Unlimited, you'd likely have something very similar. Lite nodes would likely not detect the hardfork, so you get all of them automatically. If you can also convince the exchanges and merchant service providers (like BitGo) to switch over, and then you get a majority of the hashrate, you're going to have the economic majority. And that's a problem for decentralization, because it basically means that you can win the economic majority by winning all the centralized services who stand to make a ton of money. You get a picture that's perhaps reminiscent of this:
Bitcoin's reality today is that the economic majority relies on centralized services. If you can get agreement from the 2-3 largest miners, the 2-3 largest exchanges, and the 2-3 largest payment processors (like BitGo), you're going to cover substantially more than a majority of the Bitcoin users in the ecosystem. It means that if you are letting the economic majority do the voting, full nodes don't really mean anything. Your full node only counts if it's powering thousands of wallets doing millions of dollars in daily transactions. You give up control to the centralized few.
But that's not the bad part. The bad part is that when these centralized players decide to raise the block size, they raise the requirements for participating in the ecosystem. So now you go from being able to run a full node that represents practically no economic power, to not even being able to run a full node, which means you have to trust one of the centralized services that can. But that's still not the bad part.
A time is going to come when Bitcoin is going to want even more scale. So the economic majority begins voting on what the new block size should be. Only this time, all that remains are the centralized services. And most of them can handle the new increase, but at this point the scale is large enough that some of the smaller centralized players can't keep up. Because the new block size requires a small data center to keep up with, and you just can't afford that if you only have 100,000 users. But these smaller players don't make up the economic majority, and they would if you could include the full nodes from before, but those full nodes are long gone, eliminated in previous block size increases. And Coinbase really wants this upgrade, is really pushing for this upgrade, and the rest of the economic majority agrees it's a good idea. They are the ones with the power, so without consent of the users of the ecosystem they decide to increase the block size and increase the scale of Bitcoin. And they push out their smaller competitors.
See where this is headed? Not only have the everyday users completely lost control of Bitcoin, not only is Bitcoin controlled by a small number of centralized players, but the number of centralized players in control is shrinking, because every time scale becomes an issue, the biggest players are able to push through scale as the economic majority, and the next round of smallest players is eliminated. Soon, you've only got 2 or 3 centralized entities left who are capable of keeping up with Bitcoin's scale, and everyone else is left trusting them. And 2-3 massive entities are much easier for governments to regulate and manipulate, and Bitcoin now resembles a modern bank, except for having unique roots.
The crux of the problem with Bitcoin Unlimited is that the economic majority is making the decisions, including the decision of who gets to be a part of the economic majority (by increasing the cost of participation). Those in power can use that ability to bring more power towards themselves by making the system too expensive for the less powerful to participate. This is a massive centralization pressure, and would be a disaster for any cryptocurrency with decentralization as a goal.
If you like decentralization, you should dislike Bitcoin Unlimited. I feel it necessary to say that Bitcoin Unlimited has many problems besides the one I described here, but this one is the most significant and most unresolvable. If you want to scale decentralized cryptocurrencies, Bitcoin Unlimited is not the right solution.