What will happen to my bitcoin if both Core and XT remain indefinitely? I have some bitcoin in wallets and online accounts in multiple places. What will happen to this bitcoin if both Core and XT remain indefinitely? Will I own twice as much bitcoin, just in two different currencies?
Ultimately I believe the chain with most work should be the valid one, suppressing all other chains. In fact if you use an SPV client, such as MultiBit, you don't even check the size of the block, because you only use the headers. So if that's the rule, your money will only ever be in one chain: the one where most computing power was used to generate it.

PoW is entirely democratic: people vote with their computing power and if more people decide they want different protocol rules, so be it. In fact I would go even further and say that this is much more democratic than a bunch of developers deciding what the Bitcoin protocol should be.