Religious exemptions are available, but federal contractors will accomodate such religious exemptions by placing the exempted employee on un-paid suspension (and requiring such employees to paid the company’s contributions for their health insurance) until the company decides how to handle the situation, unless the exempted employee voluntarily resigns in the meantime.
Problem solved.
Imagine if an employer hired 200 people, including 10 Muslims, but then put the Muslims on “unpaid suspension” because they insisted on taking Islamic holidays off. That plan would be shut down within hours in any Federal court.