The overwhelming perception seems to be that what they want is to have their cake and eat it - it's implied from what they say on their website. So yes they have some support but staying royal but only doing the appointments they want but being free to cash in on their titles implied from what they have expressly stated isn't palatable to a lot of the British public - as demonstrated by the posts on MN and comments on online newspapers. The way they went about it too - announcing it before telling the RF and getting their agreement - is sneaky and they've justly been criticised for that.
They are not really minor royals, despite Harry being sixth in line. He's 6th in line to probably the most famous family in the world. They generate a lot of press, good and bad, around the world. Giving them what they want won't allow more privacy.
They have privacy in their private lives anyway, when away from work. I don't see them in the press going about their business, popping to the shops etc, do you? And they don't want privacy - they still want to be in the public eye, they've said that themselves.
It won't be a win win because as I've said before and many others have it opens up the potential for the RF to be embarrassed and criticised, as per the red carpet/Disney hustling. If that is an example of them doing what they want - finding jobs like voice-overs for money then it is not changing how the RF operates for good. Look at the criticism it has generated. If the RF allow this then they are in a sticky situation with the public.
I wouldn't mind if they wanted to step down and be private members of the public. H&M don't want that. They want their titles and to be members of the RF, collaborating with the RF etc, but be free to live and work in North America to set up a foundation perhaps, do commercial work for their own gain to be financially independent etc. That is not wanting privacy.