You can do a wedding under any theme you like. What can’t happen is the actual wedding part. That has to be performed either by a registrar, or if your wedding is CofE, the vicar can do it.
So, they could hold the wedding in their temple, but there needs to be a registrar present to do the actual deed. You will see the same thing in any other kind of wedding - civil or religious. Sometime, the wedding itself will be done in the registry office, and the ceremony held elsewhere (this was certainly true of the Humanist wedding I went to once).
