My cousin converted to Islam a few years ago. I only see her occasionally. At my grandmother's funeral she refused to shake hands with several unrelated men saying that she was not allowed to based on her religion. Up until then I'd only seen her with her dad & mine. Since she's related to them touching was allowed & I did not notice any particular restraint.

Not being willing to shake hands or greet someone hardly seems to rise to an issue of legality. By our standards it seems rude but little more. If he's not doing his job, that's different & needs to be addressed by the employer & 'reasonable accomodation' worked out if possible.