I don't think it is "mindless fear" to point to Ethereum's failed hard fork and point out that it permanently split the network. This caused significant losses for custodians---Coinbase lost ETC and still hasn't repaid their customers. BTC-E was replay attacked and lost all of their customers' ETC; they won't be repaying it. The results would have been disastrous if Kraken and Poloniex didn't have the foresight to ignore the Ethereum Foundation's advice to ignore ETC and not repay their customers their money. Replay attacks were commonplace, and many users lost money in trying to spend on only one chain or the other.
Seems like mindless fear to me, the replay attack has been fixed on all of the proposed Bitcoin forks, it is rather trivial to fix actually. The ethereum foundation purposely decided not to fix this particular issue, I thought that was a mistake. Splitting Bitcoin as a minority would not cause such problems at all, custodians also need to be more responsible in such a situation and take it into account. Some of those custodians simply just did not believe ETC would survive, now we know better.
The effects of splitting the Bitcoin network and increasing the supply of "bitcoins" across multiple blockchains could be far worse for Bitcoin's value proposition than a network split in Ethereum.
Splitting the network does not worsen Bitcoins value proposition, since the share of total Bitcoins remains the same across all chains for investors, which means it does not create any type of monetary inflation, it protects the value of investors. Furthermore because it is already relatively easy to do this with a small minority it should already be a part of Bitcoins value proposition, if you are not taking this feature into account you are not truly evaluating the value of Bitcoin, for me it actually improves the value proposition of Bitcoin since I perceive this feature as being a crucial part of the governance mechanism.