As far as I know it is not possible to remove VLAN 1.
The best practice is to remove all ports from VLAN1. Anyway in your scenario I suggest two possible solutions.
Move the customer to a different VRF or using SPB VLAN/ISID mapping so that the connected customer
can do stupid thinks like using VLAN1 and you have the rest of the network encapsulted so that you
can ignore everything that the customers is doing in his part of the newwork.
Cheers