I know the 1MB is a hard limit which affects both miners and clients. I'm assuming a world without MAX_BLOCK_SIZE at all, both miners and clients.
Miners can ALWAYS drop a valid block if they don't like it, just like ignoring any valid transaction. Currently, miners taking non-standard transaction has higher risks of orphaned block because other miners may not like these block.
If a miner (Bob) sees a new valid block with height N but doesn't like it for whatever reason, he will simply keep mining on top of block N-1. When Bob finds another valid block (N2), he will broadcast to the network and other miners will choose one between N and N2. Here Bob takes a risk of being orphaned because other miners may build on block N. If block N+1 is built on N, Bob has to reconsider the risk and he may decide to keep mining on N+1, instead of N-1 or his N2. However, if Bob (or his team) owns 51% of the network, he will always win and block N must be eventually orphaned. (You may call it a 51% attack but this is exactly how the system works)
Therefore, if the majority of miners do not like 1GB block, building 1GB block will become very risky and no one will do so.
What you are describing is much worse than a mere fork, the only word I can think of for it is a
shatter.