If the BitCoin economy is mostly only applicable to libertarians, it won't be all that large.
If other people are happy with whatever features of BitCoin remain under centralized control, more power to them. I see no problem.
But you're saying we have to fear that someone will start effectively issuing p2p dollars. I think it kind of defeats the purpose, but I can't see why that's a more of a threat to the principles of Bitcoin than plain old USD.
If the new network implemented inflationary logic, as a modern state is wont to do, I can't exactly see people rushing to convert their old (relatively stable, perhaps deflationary) money to the new one. Therefore, I can't see many businesses stopping to accept the old bitcoin.
And after whatever adjustments are made, it will be business as usual. Bitcoin will remain the network for people that want a decentralized currency. Not necessarily of libertarians, but of anyone with distrust or disillusion with their governments and the banking system. Which I don't think is such a small demographic.
Rushing to convert "old network" BitCoins into the new network (or dollars, or whatever), and businesses stopping acceptance of them is exactly what will happen. Don't forget the primary function of money is to allow people to trade it for things they want. Unless you're a staunch ideological libertarian you will want as much of your "money" as you can get in whatever system offers the most goods and services. Otherwise you have lost value. That system will certainly not be the one containing only sparsely geographically spaced libertarians.