I don't know about that. People would still be holding their original Bitcoin, so maybe they'd be okay just ignoring the HF and continuing. It might be less accessible for newcomers but that doesn't mean that people will lose trust in cryptocurrencies in general.
Bitcoin, let alone anything else, is still in the extreme sceptic phase for most of the world. The only way you convince more people that it's here to stay is by remaining progressive, unified and dependable.
If it splinters into a myriad of screechy chains all changing PoW, dumping and 51%ing each other then that looks like just another failed project to everyone who already believed that anyway.
BTC still has an awful lot to prove and that goes just as much for the people who are already involved in it, let alone future arrivals.
As Mr W pointed out above, an ETH style split would be a dream scenario but there's too much money and power on the line for that. Everyone will be scratching each others' eyes out for that one chain.