Can health care workers, school personnel, higher education personnel, and higher education students choose to be tested rather than be vaccinated, even if they do not meet the requirements for a medical or religious exemption?

Yes. If you are required to get vaccinated (because you work in healthcare, at a school, college/university or state-owned or operated church or place of worship), you do have the option to be tested weekly instead. However, your employer may have stricter requirements.