Do electric charges increase activation barriers?
Here is a specific example from biochemistry. In the hydrolysis of ATP, the first step is the attack of a hydroxide anion at one of the phosphates. The triphosphate portion of ATP has multiple negative charges at neutral pH, so this reaction is very slow.

When catalyzed by an enzyme, the enzyme often binds to a magnesium cation in such location that it shields some of the negative charge. This makes the reaction proceed faster.


  Do electric charges increase activation barriers?


Yes, they do. And there are various strategies to lower the activation barrier in these cases. One is providing a counter ion as described above. Another is to change the charge via acid or base catalysis, i.e. protonating or deprotonating one or the other reactant to decrease electrostatic repulsion.


  Would the former have a lower activation energy since there is no repulsion between the molecules? 


Yes, and it would be sufficient to remove one of the charges in the latter to lower the activation barrier because electrostatic repulsion requires both particles to be charged.