Are the mining incentives of bitcoin compatible with the existence of a competing Proof-of-Work chain? Scenario A: A chain split occurs due to a bug or contentious rule change (i.e. the miner incentives aren't changed in any way).

Both coins initially start out with the same difficulty (and won't change for another 2016 blocks, in the worst case), but their market price will vary.

A rational economic miner will only mine the chain with the highest reward, which is the chain with the higher market price. Users of the lower value chain can offer high fees to compensate, but this is costly.

Scenario B: A hard fork chain split occurs where one chain has decreased difficulty and/or higher block rewards (not touching the 21 million limit, but pushing the release schedule forward).

Unless the new chain has a really low market value, miners are highly incentivized to mine it. It will be hard for the old chain to compete.

The question for both scenarios: How will the scenario play out? Can both chains coexist or will the less popular chain die from a negative reinforcement loop (lower value -> less blocks mined -> even lower value) and be forced to do a PoW hard fork?

And if both chains can't coexist, does that mean that any chain that tries to out-compete bitcoin for the same PoW is a threat to the network?
Both chain in your scenarios can coexist because the current value of a coin (and the current mining reward) isn't the only factor miners are taking into consideration when they have the choice to mine two different coins.

They also put their personal conviction into consideration when choosing what to mine. If they prefer the change brought in chain A, why would they mine chain B that doesn't have it ? (Mining chain B in case of a HF would be being against chain A in that case)

So yeah both chain A &amp; B can coexist as long as the differences between them are big enough. If not their would be no incentive to choose to mine the chain with the least value.