Is teaching for a biology program without "specialized accreditation" bad for your career?
In my experience, very few biology programs are accredited, for example at liberal arts undergraduate colleges. But they're still important, since liberal arts students still ought to be exposed to biology. So I don't think that association with a good quality teaching program will hurt your prospects as a teacher, but unaccredited programs tend not to engage in research very intensively, if at all. So as others have mentioned, you should probably consider a post-doc at a research school if that's your goal.