The best LORs are the ones from people who know you well and who are in a good position to judge the quality of work. For this reason, AdComms like letters from professors, especially for applicants coming right out of college.
If these politicians and judges don't know you well, then their letters won't count for much. AdComms aren't impressed by famous or powerful letter writers. But if they do know you well, then go for it (but I would still suggest getting an academic rec as well).
On a side note, this post should probably be under the "Recommendations" thread.