I’ve worked in CS for many years and have yet to have anyone question what courses comprised my degree. I graduated from a small Catholic liberal arts school (so small many upper-level courses were offered only every other year).
The most important thing I learned is that most of what you learn in your classes is not going to be directly applicable to a job. The more so the further out you get from graduation. You need to learn the concepts, but most importantly learn how to learn and understand that CS is a field where you never finish learning. I never took a database course - yet spent several years working in Oracle. The technologies I work on today did not even exist when I was in college. I have gone and taken courses here and there to “fill in gaps”, but that’s because courses like Web Design and User-Centered Design did not exist when I was in school. And the writing and critical thinking skills I learned at a liberal arts institution have been very valuable.
There are sure to be some employers out there who will want the uber-technical people and who will look down on the degree from the liberal arts school - but there are many others who will value the broader skill set. You need to think about what type of school is the best fit for you. I knew I wanted a technical major, but I also knew I wanted the wider range of opportunities offered at a school with significant core requirements and where it was easy to take courses outside my major.