To be clear, humans are forbidden from entering Doriath. Noldor who are not related to Finarfin are forbidden from entering Doriath. Sindar are welcome, and Dwarves have been invited in, but the Girdle is pretty strict, and Beren is clearly in violation of the laws of Doriath for being there.
One could make an argument that he is a refugee and should be granted special status, but that is an argument that would need to be made to the king to change the current policy, not an existing loophole or exception. So far, no exceptions have been granted, even when refugees were actively fleeing battlefields in the Dagor Bragollach.
So at the end of the day, it is Lúthien's judgement call coupled with the decision of the Girdle itself to allow him through that makes the exception for Beren, not his (mostly) unarmed status. The fact that he is passed out when she first sees him certainly makes him as non-threatening as possible in that moment.