Core courses meaning English, algebra/calculus, fine arts, literature, world civilization, physical education requirements and non-science electives, then absolutely not a problem coming from a community college.
Core courses meaning biology, chemistry, genetics, organic chemistry, biochemistry, microbiology, and other required sciences courses, then there may be limitations depending on the school. For example Oklahoma requires organic chemistry, genetics, nutrition and biochemistry be listed as upper division course and be taken at a 4 year institution. But other schools have zero requirements at 4 year institutions.
That said, I took physics and microbiology at CC and, honestly in both cases the classes turned out to be really easy. I imagine that is not the case for most course, but it did happen for those. But, more importantly, it did not effect my acceptances.