If all the non-mining nodes reject the block, then the vast majority of the network doesn't have a copy of it. It basically isn't a real block.
The network worked before there were ever non-mining nodes having a copy. So if only the miners have a copy of the transactions then it is more than good enough.
Your example is like a straw poll. The non-mining nodes had no real authority to actually enforce their conclusion.
Like I said the only vote that holds authority is if you win a block, then your vote on the previous block validity counts as a confirmation.
Sure the nodes have authority, as a group. If a miner violated BIP 148, they would have been forked off of the network, losing hundreds of thousands of dollars. If some miners want to make their own chain that breaks the rules of all the rest of the nodes, they can do that. But it will result in a currency split, creating two currencies, one where the miners are playing pretend and the other which was and still is the real bitcoin, where all the rest of the miners are still making money. That's if the dissenting miners aren't driven into bankruptcy before they can even confirm their own blocks, in which case it doesn't affect anyone else and there is no currency split.
How do you fork someone off the blockchain if you yourself do not create the blockchain? The only way you can fork someone off is by mining faster then them on a different chain. Yet non-mining nodes cannot do that.