Would a specialized cs major (bioinformatics) negatively affect chances for general cs jobs?
I don’t think so in the least! Think about it this way. Programming is one of the few fields where you don’t need to have a degree to land a high-paying job. People these days can get hired on the strength of a GitHub profile alone.
A CS degree is a “feather in your cap”–an added bonus. In our economy today, we pay more for specialization. I would try to use a CS degree in bioinformatics to my advantage in a couple of different ways.
First, when interviewing for a non-bio-specific role, I would point out how rare bioinformatics degrees are compared with the already highly competitive CS degree. Second, I’d do some research and create a list of target companies in the bioinformatics space.