Now there is a rule that employees aren't allowed to wear head coverings at work (for whatever reason)
And maybe that rule is the stupid one.
So if one religion is allowed to claim special status for their head covering (Head scarf), can an orthodox jew wear their hat? Can someone believing in druidism wear antlers to work?
Except it isn't necessarily claiming a special status.
The argument can simply be that the headwear ban should be removed, unless there is good reason for it. So yes, anyone can wear any headwear, so long as it doesn't interfere with the task at hand or other people. The antlers would probably fall afoul of those requirements.
And what is with people who happen to have no religion they believe in. Why are they granted less rights by the state than the religious people?
They wouldn't be. The removal of a ban doesn't somehow mean that atheists have fewer rights. They'd be allowed to wear their desired headwear too.
So: Which other possibilities does a state have to resolve this besides
Still a false dichotomy here.
To be clear here: the second option is not "ban religious symbols alltogether", it's "we have our rules, there is no way for you to get an exception with the reason 'religion'"
The option is not to allow "religion" to be used as an exception, but rather set rules that are permissive to everyone, including religious people, within the limits of the task at hand and inconvenience to other people.
A headwear ban is pretty clearly discriminatory towards Muslim people, and probably also to certain Jewish people though I'm not 100% sure of that. The goal should not be to give them exceptions, but rather rethink the headwear rule.