Absolutely. If one wishes to race under the auspices of an organisation dedicated to the sport of motorcycle racing, one could hardly be surprised if they wish to consider your vehicle as a motorcycle.
It may be a bit of a faff, but a rear view mirror has got the capability to cause a great deal of damage to you in a crash, and it is sensible to require their removal (as should anything that could cause injury and isn't necessary for the safe operation of the vehicle).
You'll be needing to take a set of tools with you anyway to check the car over, adjust the tyre pressures, and so on, so an extra half an hour whipping off the lookbackascopes isn't too much extra effort.
BTW, doesn't the ACU require that oil drain plugs are lockwired? They always used to when I was hill climbing?
And look on the bright side - if you stuff it into the bushes, at least you won't damage the mirrors!
