Oil-Stained Wolves are almost certainly safe since we know the effect persists through death, and we've been allowed to keep them through a number of major patches and one expansion. The only thing that takes away the oil slick effect is bringing them to arenas.
Can't speak for any others, though, as I haven't any besides those (the oil-stained wolf and ghostpaw alpha).
Eziwolf wrote:Edit: I just saw an oil-stained Wolf pet in Orgrimmar, so they're safe
It's too early in the beta to tell.
Kidding. If they were going to fix the oil-stained wolves they'd have done it long since.
As for the taming method... On Lost Isles I did try the quest taming method on them for hours and couldn't get it to work. They'd either despawn or tame without the oil.
Two things seem to be important about the quest taming method
1. The quest makes them follow a script -- you toss them the meat, they run forward, howl, eat the meat, poop and run off.
2. At about 15% haste, the timing on the despawn required me to start taming when the wolf started to eat. The taming bar would disappear as the wolf started to run off, but the taming animation would keep going until the tame was successful or the wolf despawned.
For the taming animation to keep going through to the scripted despawn... that feels like a fix to prevent that taming method.
I also suspected that freeze trapping them might affect the despawn timer, but it doesn't seem to make a difference.