Entropy - Negligible?
This difference in Gibbs Free Energy is only due to entropy right?


This is mostly true.  (I think it is 100% true when concentrations can be used in the reaction quotient $Q$, but am not sure if it is strictly true when solutions are not ideal and activities have to be used instead.)


  Because enthalpy is a constant? 


Enthalpy is a "constant" only because of the way electrochemical standard states are defined.


  So obviously, entropy significantly
  interferes in the process of electrolysis. 


Have no idea what this means.  How does it "interfere"?


  And yet, it is ignored in
  virtually all spheres of chemistry. 


False.


  I'm beginning to doubt my chemical
  intuition because of entropy effects, and faith in it can only be
  restored if entropy really was negligible. So it is negligible or not?
  If not, why is it always ignored?


It isn't negligible and is not ignored.