It would seem that mandatory Bible reading (or any other religious reading) without accommodating divergent religious beliefs would be a violation of Title 7 of the 1964 Civil Rights statute if it resulted in any negative employment action. Voluntary religious readings may have a different result unless the employee is rendered an "outcast" by failure to participate. I can visualize such a charge. An even finer line however would be courses concerning "total well being" or the alignment of minds, bodies and spirits with the mission of the organization. Trying to draw a line between spiritual and religious certainly can be done, but needs to be embarked upon very carefully.
One expert urges employers that do engage in "New Age Training" to provide an alternative for employees who object to the spiritual or religious overtones of such training. It may, however, be a problem to find a non-spiritual alternative. Some New Age Training is offensive to both conservative religious individuals or non-religious people who do not want a religious element introduced into the workplace.