Yes I would. Except for the safety concerns that Richard Wee already mentioned, I see no reason not to. If you want to wear a cross or crucifix, a yarmulke or turban, that's fine too.
I've encountered two postal clerks who wear Hijabs in my local post office. If any customers were harboring anti-Muslim sentiments, those sentiments were overcome by the women's competence and efficiency which far exceeded their more experienced, seniority-protected white male counterparts dressed in regulation uniforms.