Also, are there any exceptions that you know of?
Since you are talking about hydrophobicity I am assuming you are interested in liquid-solid friction. If you are interested in solid-solid friction I can say only one thing: hydrophobicity and solid-solid friction are in general unrelated.
So for the liquid-solid case. I am going to give you an answer that gives some insight, but no concrete rules, because, as far as I know, there aren't any.
Superhydrophobic surfaces typically have some surface structure that allows the liquid to 'float' partly on air and partly on top of the surface structure . Friction is related to the amount of contact area where there is a no-slip boundary so that will decrease therefore friction will be lower. A cool application of this effect can be found in this 2013 PNAS article by Karatay et al.
However, if you have a droplet moving, instead of a full liquid stream, then there is a counter-acting effect which is called contact angle hysteresis, which allows a droplet to sustain a difference in contact angle at the front and back of the droplet. This causes a force counter-acting motion of the order of the surface tension of the liquid $\gamma$ and the difference between the contact angles $\Delta \theta$: $F=\gamma l \Delta \theta$, where $l$ is a lengthscale of the order of the droplet radius. This force basically acts as a static friction on the droplet.
The value of $\Delta \theta$ is a complex function of the amount of surface roughness, being 0 for a atomically smooth surface but also approaching 0 for roughness with a small typical lengthscale. Therefore it is hard to make a general statement whether superhydrophobic surfaces will have a lot or a little friction. It all depends on the details of the surface roughness.