Him & a vocal community (/r/btc) appears to believe in that. What gives BTC (and /r/bitcoin) the right to the name Bitcoin considering both are forks from the original chain?
You own your Bitcoins in the full meaning of the word. You fully control them, by way of your private key, but you also trust that the rules of Bitcoin won't change. The former ownership is technical but the latter is social.
There is an implicit social contract towards anyone who buys Bitcoin to be able to spend them any time in the future, under the same rules as today. That includes not having to upgrade to another ruleset with arbitrary changes.
For this reason it was important that the block size increase was made opt-in, and that any hard forking fundamental changes that are required in the future are trivial or have pretty much unanimous support.
That said I personally don't believe that the name will make a difference in this battle.
What happened on block 494782 was also a fork in some respects, there was well telegraphed plans to change the consensus rules on that block, but no one mined/accepted blocks with those rules.
You're mixing up soft fork with a hard fork and implying that soft fork is somewhat better, when in reality it is just technical concept and has nothing to do with it.
Actually in current situation we already have example, the soft fork (SegWit) implements a complex mechanism to add segregation witness feature and allow for off-chain transactions.
The change in Bitcoin Cash is simply raising the block limit to 8MB. In fact initially bitcoin had no limit for the block size and the limit was added to prevent DDoS.
That limit was meant to be increased as there would be higher demand.