Wearing a veil at work: what are my exact rights?

I have colleagues who wear the veil and honestly it really depends on your sector and what country you're working in. In France, your employer can only ban it if it's justified by the nature of the job (like a position with direct customer contact where the company applies a strict neutrality policy) or for safety reasons. Otherwise, it's discrimination, period. I'd advise you to check your company's internal rules, and if you're unsure, contact the labor court or a union to find out exactly where you stand.