once you start a PrC, can you lose its requirements and still continue the PrC?

[Jhaelen]

Or ignore your interpretation of the rules and allow Assassins to be non-evil as much as they want.

Sure.
Though it's not a question of interpreting the rules regarding prerequisites for prestige classes.

It's more a question of interpreting what alignment means in your game. If I was using Eberron as a setting I'd probably remove any alignment requirements.