So it depends on why your program is not ABET accredited. If it is a reputable foreign school, there probably won’t be an issue. If it is because the program isn’t rigorous enough, then you have problems. If it is because the program is new and in the process of being accredited, then it is more of a crap shoot.
Problems in terms of higher education and employment isn’t because the school isn’t ABET accredited, but because it is new or not rigorous.
Not getting an ABET-accredited degree can present a significant problem in getting your P.E. license.
It likely would not significantly affect your opportunities for employment, because I wouldn’t expect most employers to be familiar with what programs are accredited or not. It may limit your chances of advancement, however, if your field is one in which getting a P.E. license is required to advance. This is primarily only the case for those fields that work on projects directly affecting the public, though, such as civil engineers.
Finally, most graduate engineering programs that lead to an M.S. or a Ph.D. degree are NOT accredited, even those from major, national universities. Generally, only B.S. degree programs are accredited by the ABET. (So getting a B.A. instead of a B.S. can also present problems with getting a P.E. license.)
Incidentally, I see in your OP that your refer to both a “Bachelor’s in Electronics/Electrical engineering” as well as “EE technology.” Note that engineering technology degrees are generally considered a step down from a true engineering degree, being somewhere between engineering and technician training.
Engineering technology degrees do not always qualify as the requisite education necessary to get a P.E. license, depending on the state, or may require additional years of experience. The same is true for a non-ABET accredited engineering degree. Depending on the state, the number of years of additional experience required to get one’s license may be significant.
My current employer and many that I’ve interviewed at recently require an ABET degree to be hired as an engineer. As noted above those who have “technology” degrees are somewhat limited in their advancement opportunities, although it doesn’t seam to be as big of deal as what was in the past, in my experience.