Not overriding the default (z-index: 4) fixes nearly all of them. Anything else, the rest of ooui probably needs a skin-specific fix anyway, so that's kind of on the skin to sort out.
Some skins avoid this by having different layering, or explicitly setting their own overrides, but removing this doesn't seem to hurt them either.
Affected skins from a brief check: GreyStuff, Example, CologneBlue, WoOgLeShades, quite a few others
Unaffected skins: Modern, Timeless, Vector, MonoBook
(Seriously, if it's broken in Example, we have a problem. Example barely even has any styles to conflict with.)