I don't see how a hard fork is somehow not Bitcoin. It's simply an upgrade. A bigger upgrade, but an upgrade nonetheless. If it is done in the face of serious controversy and there is a real split, then there is a naming problem. Otherwise it's just as much Bitcoin, just a new version.
It could be Bitcoin version 2.0 for example. If there is a permanent split, then the other network would be called something else.
I'm going to side with the version where the block size limit is raised, that is for sure. If it is done in a smart way though, it's a big change and needs to be thought of carefully. I don't advocate "just raising it", I advocate planning the change well and thinking about the long term future as well.
Changing the protocol is not the same as changing the client. Software becomes so cheap and even free is just because they could always come up with a new version with new features etc... This is the view of a service provider, not a central bank
Bitcoin gained big success just because it is can be trusted, but people certainly do not want their trust to be easily changed by a group of designers at will
Before, I support the change to protocol in a carefully planned way to improve the end user experience, but recently I discovered that you can double spend on both original chain and the new chain after a hard fork, then it means the promise of prevent double-spending and limited supply is all broken, that is much severe than I thought