Christianity does not prohibit Christians from hiring Muslims, but Islamic countries routinely discriminate against Christians. So this group has it backwards.
The Muslims are only speaking from the experience they know, and if the situation were reversed, for sure the Muslims would turn away an avowed Christian. Or Jew. Or peyote-smoking Native American.
People are hired for the value they can bring to the enterprise. If once hired, they fail to meet expectations as to work ethic, out they go. Every employee, regardless of religious conviction, is called upon to fulfill their defined mission within the organization. If that person cannot, or will not, comply with this modest demand on their talents, then seek employment elsewhere, but certainly depart what would only be a hostile work environment.