What's the best word (or words) to describe rubber's 'gripping' property that is the opposite of oil's slipperiness?
It's not 'rough', since rubber grips without necessarily being rough.
The "obvious" answer is grippy — the ability to grip a surface well. It is less commonly used than slippery, but it is a proper word.
As has been mentioned in comments, "sticky"or "adhesive" might fit. But the truth is rubber isn't naturally sticky or adhesive. It does have a high "coefficient of friction" though. That's why it isn't slippery. In non-technical terms, we can say rubber is nonslippery or skid-resistant.
The word tacky is used when describing the 'grippiness' of golf grips (which are, as it happens, made of rubber), especially when it comes to the 'stickiness' of the rubber compound, as opposed to the roughness of the surface.
The word slippery implies very little friction. You want a word that implies a lot of friction, which creates a "gripping" sensation.
To that effect, I couldn't find any simple, commonly used words. Frictive is one, which literally means "friction-y". CarSmack suggested "rubbery", but "rubber is rubbery" seems redundant.
Comments thusfar (including the OP's) seem to confuse friction with rheology. A slippery substance is one with low viscosity, not a low coefficient of friction. A coating of oil makes surfaces slippery because the oil deforms easily and permanently under small shear (i.e., sliding) stress. Rubber deforms only slightly, then returns to its original shape, so a rubber coating does not makes surfaces slippery. At the molecular level, both rubber and oil cling to many types of surfaces on contact, but the difference in slipperiness has to do with the way that the two substances flow.
You can say that oil is plastic (deforms permanently), while rubber is elastic (restores to original shape). Alternately you can say that rubber is viscous (deforms only slightly), while oil is slippery (shears easily). A less technical term for rubber would be skid- or slip-resistant.
Unslippery is certainly a possibility, but I don't like it.
Commercial products such as deck paints tend to use terms such as "non-slip" and "slip-resistant".
The first word that comes to mind without trying too hard is chafing. Perhaps you could also try abrasive. While they are not perfect matches for rubber to describe the equivalent of slippery to oil, it is a close match.
Rubber is 'tacky'. I like the word tacky. It's kind of tacky like blue tack or the soles of your 'tekkies' (slang word for running shoes in Afrikaans)...
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