If you're looking back on an instance where fear of heights may have prevented you from moving forward with something that you now wish you had moved forward with AND your fear of heights has since vanished, then saying:
I wish I hadn't had Acrophobia.
would make sense. Saying you wish you hadn't had it suggests that you no longer have it. It's tantamount to saying, "I wish I hadn't had Acrophobia at that time," which can either mean you experienced a unique moment of Acrophobia that you normally do not possess OR that your Acrophobia is no longer with you in the present but was in your past.
But if you had and still have that fear, then simply saying:
I wish I didn't have Acrophobia.
would make more sense. Saying it this way you're still considering your fear as a current obstacle, but also still covering your bases for having it in your past. You're reminiscing (perhaps regretting a moment) by addressing the fear you still have.