I struggle with stuff like this.
I strongly defended and will continue to defend to this day the right of a Christian baker to refuse to bake a wedding cake and set it up at a gay wedding. The gay couple had been long time customers and were treated as friends in the place when they came in for other products offered for sale. But the baker did not believe in gay marriage and should never have been forced to participate in something he did not offer for sale and went against his religious beliefs. But that was his business, his turf.
Employees who work for somebody else should expect to follow the protocol, rules, regs, including wearing uniforms established and provided by the employer however unjust, ridiculous, improper, or wrong they may believe those to be. If they have religious objections to any of it, they should amicably resign and move on. Their employers should give them letters of recommendation if they are good employees, but, however much of a jerk it would make him, he should not have to accommodate the religious convictions of his employees.