Yeah, I can see that. As a principle, I agree with it, but I'll put it behind (or maybe on-par with) the principle of identify and embarass fascists at every opportunity.
I see your point, though I don't think there are many people who would see this and think "oh wow, he did a nazi salute? Oh...he didn't? Well now I don't trust the people saying he's a fascist." If a person can't see his actions and words from what they are I don't think we're winning them over anyway.
If there is a job for a british monarch to do it is to return stolen property and apologize all day every day until they die or abdicate. Anything such a person does to enjoy themselves is spitting on everyone whose murder and suffering made that enjoyment possible.
The only exception being a good shit. They should be able to do that in peace, and that's something they can do without access to their stolen wealth.