Is ABET accreditation important for a bachelors degree in software engineering? Would getting a non ABET accredited degree in Software Engineering put a person at a considerable disadvantage when it comes to employment, or applying for graduate school?  I ask because I was accepted into San Jose State Universities Software engineering program and have learned that it's not ABET accredited.
My experience is that ABET accreditation is generally not very important, in the fields of software engineering and software development.

If the University program is well-regarded by employers, ABET accreditation is not important; their positive impressions will outweigh any accreditation.  If the University program is poorly-regarded, ABET accreditation is not going to make up for their poor impressions.  If the University program is unknown to employers, they will probably look at other measures first (like past projects you've done, your performance on a phone interview, etc.) before they care about ABET accreditation.

What is important is the quality of the undergraduate program.  Since you are choosing among multiple universities, you should be looking carefully at the quality of their programs.  While it's true that ABET accreditation is potentially a signal or indicator of quality, I don't think it's a very good measure of quality.  (I know of some extremely high-quality computer science programs that are not ABET-accredited.)  Instead, to decide where to study, I'd be looking closely at the programs, to assess their quality in as many ways as possible.