[ai-danno]

If your connection on the switchport to your server is set to 'access' already then that 'access' functionality already strips the VLAN tag- hence why your box doesn't need to have knowledge of the particular VLAN of which it's connecting switchport belongs. However, having the switchport set to 'access' also means that only one VLAN (aside from perhaps the management VLAN- of which functionality varies from switch to switch) will be able to be assigned to your switchport.

If the switchport (and OBSD NIC) are set to 'trunk' then the OBSD NIC will have to be configured to talk to each VLAN that the connecting switchport is assigned to. Any VLANS that it is not specifically configured to talk to in this instance will not be available to communicate with.