Posts have been made before that assert the tip hardness has nothing to do with cue ball squirt.
I do not have a robot to prove my position, but I believe that theoretically, a softer tip should result in less squirt.
The reasoning is a bit lengthy, but here goes:
A softer tip should have more friction on the cue ball than a harder tip. Why? Well, imagine an infinitely hard tip, or at least a tip as hard as a ball. I think everyone here would agree that ball-ball friction is generally less than tip-ball friction. (If someone disagrees with that assertion, please explain why.)
More friction at the cue tip transfers more of the axially-directed force of the cue stick to the cue ball, ... than less friction at the cue tip does. Think of this as the "throw effect" between the cue stick tip and the cue ball, analogous to the "throw effect" of a dirty/sticky CB on a dirty/sticky OB. We all acknowledge the effect of throw is to divert the OB a little bit from the contact line and toward the line of the original CB direction. By the same reasoning, friction between the cue tip and the CB results in diverting the CB a little bit off of the contact line and toward the original cue tip direction. (This is why squirt is not as big as the contact line between the cue tip and the CB.)
To me, a softer tip means more friction, and more friction means less squirt.
Whether the difference between a hard or a soft tip can be measured or not, I am not sure. But this is my position and I am sticking to it.