You're missing a major component of the law:

> Title VII of the Civil Rights Act of 1964 requires employers to make reasonable accommodations for an applicant or employee whose sincerely held religious belief, practice, or observance conflicts with a work requirement, *unless providing the accommodation would create an undue hardship for the employer.*

If using a computer is necessary for the job, then the religious exemption would create undue hardship. Presumably for this Kentucky guy's job he can get his work done without AI and the university isn't suffering for it.