Closing. You've cross posted this in multiple forums and they've already given you answers. You'll find a simple search of the derm forum will net similar threads with similar answers.
Can you become a dermatologist with bad skin? Sure (you're talking to one currently)
Should you fix the underlying skin condition (or improve itas much you can)? Sure (I did. You'll find that as a dermatologist, you're going to have extra help and extra motivation)
Is it silly or petty that people judge you on skin conditions? Yes, but that's life. (Would you go to a dentist with rotting teeth?)
Either way, the barrier to entry in dermatology is academic, not dermatologic. Wishing you the best of luck in both.
Closing.