For the record I lean towards Republicanism but in general I am on the fence about this specific, current H & M debacle. On the one hand, I think it must be very difficult to join the RF as an outsider. On the other hand, I can see the merit in the argument that you are either totally in, or totally out.
However, as has been stated, is there really that much of a difference between so-called "public duty" and "charity and philanthropy" in reality? The Queen and Prince Charles undoubtedly put in the work visiting hospitals, village halls, and scout huts across the country. But at the same time, their land and estates make huge profits and generate a lot of income.
Therefore it could be argued that the RF's charitable work is backed by private income too. So what's the difference (apart from practical logistics related to H & M's location, but they have already said they would be willing to travel) between doing charitable work supported by income that you generate yourself by deals with Netflix etc, and doing charitable works backed by income generated from the Duchy of Lancaster and the Duchy of Cornwall's land and estates (which, if I have understood it correctly) is private, not public money?