In general, would greater airspeed reduce the affect of crosswinds on an aircraft's directional stability or a neutrally positioned rudder's performance?
As evinced by the scattergun replies so far - there is no such thing as a general case
In fact the whole question is as good as unanswerable, couched in those terms.
In General Terms (normal flight) crosswinds (steady state) have no effect whatsover on directional stability, as mentioned above.
With a step yaw displacement (e.g. side gust or rudder input), then Altitude, Mach No and airspeed all affect directional stability.
For example, dutch-roll interactions between roll, yaw & pitch stability can vary a great deal with speed, and also altitude and Mach No.
Aerolastic effects can also play a part at higher IAS.
At lower speeds, a/c inertial effects are proportionality higher c.f. restoring forces, perhaps that is what is at the root of this question?