ABET accreditation per se is not an issue in CS. It can be relevant if you want to later take the patent exam (either an ABET accredited CS degree, or a CS degree with specified course work, including some non-CS science course work, is listed as a prerequisite).
ABET accreditation does ensure a minimum level of quality, but good CS major degree programs exist that are not ABET accredited (e.g. Stanford, CMU, Berkeley L&S CS). For the latter, check that a good selection of CS courses are offered, and that they are appropriately technical in nature (as opposed to being less technical IT-type courses; note that ABET does accreditation for IT majors with different criteria).
ABET accreditation does require some non-CS science course work. Math and non-CS science combined must be a minimum of one quarter of the usual total amount of credit for a degree, while CS course work must be a minimum of one third of the usual total amount of credit for a degree. General education requirements must also be included. ABET accreditation criteria are listed at http://www.abet.org/wp-content/uploads/2015/05/C001-15-16-CAC-Criteria-03-10-15.pdf .