That's true and plus, sometimes you'll end up working with someone else anyways. Still, I'd feel snubbed lol. Sometimes it took awhile, but eventually all profs replied back to me. It's all in the timing too.
But anyways. I'm a psychology major and I applied to two sociology programs. They just fit well. The two programs also said that a degree in Sociology is not required, though a background in social science is. I think you're totally okay with PoliSci degrees. I'm sure it'll be helpful with the policy aspects.