Most data scientists I know don't have CS degrees but instead a background in physics, biology, math, economics or statistics.

For a data science role focused around exploratory analysis, model building and idea generation (as opposed to a more engineering-focused data scientist) I'd say that a basic understanding of programming concepts and familiarity with the most essential tools (version control, Linux, Python/R) is probably enough to be accepted into a data science role. Data science degree programs are still quite novel so most companies don't expect to recruit people with such a degree, hence there are good opportunities for people with a STEM education I'd say.