I think part of the problem is that in 3rd edition, neither Consecrate and Desecrate had alignment descriptors, allowing evil characters to heal vile damage relatively easily. No longer, obviously. I think that with evil outsiders and undead, Desecrate would let them heal Vile damage (undead because Desecrate floods the area with negative energy, which powers them, and fiends because the evil bolsters them). With humans, though, it's tougher.
Hmm. Perhaps one spell (such as
Dispel Magic, a wizard's protection from evil [since the cleric can't cast good spells], or maybe even desecrate) could either weaken the evil taint or bolster the evil cleric in such a way that Cure spells could have full effect, or a reduced one? Pax's solution is also workable, methinks.
I think your idea of Vile damage not affecting evil creatures works (is in line with the Unholy Word type spells), but for some reason it displeases me stylistically speaking. It strikes me that vile damage is not
evil like Unholy Damage (with anethema to good creatures) but evil as in hostile to all life equally, so
wrong and outside the natural order that it does not heal easily.
But that's me.

You seem to view it differently, and you should go with whatever works with you and your players. On a "how the world works" level, though, I think that as long as you allow evil characters
some not too inconvienient manner of healing vile damage, it doesn't suddenly break your game world (make the Blood War entirely suicidal, and so on) or your campaign (by making vile damage the mutually assured destruction weapon).