When the job of 'figurehead' comes with job security for you and all your family, numerous palaces, being immune to prosecution from the law, half of Cornwall and all the swans - it should be a matter for public debate and or concern.
The argument made about the lack of policy input is valid - but the Royals have a lot of soft influence in politics and there is a weekly meeting between the monarch and the PM which is unregulated. We cannot prove that the monarch has no influence, we can simply infer it. In the case of the Queen I suspect you are right - I'm not sure whether Prince Charles will follow in her careful footsteps of non-interference or not - I suspect not.
I have no problem with any institution such as Government which theoretically allows anyone of any sex/race/gender/political persuasion to take part. Those people can be kept out of power by racism, but such racism isn't tightly woven into the structure itself. Theoretically anyone can win at Capitalism by overcoming the odds, the odds might be stacked in their favour or not - but the same is not true of becoming 'the monarch'. With the best will in the world, nobody who is Black or Asian can become the monarch. It being a position of meaningless figurehead or not is irrelevent to the argument in question. If it's so meaningless, we should let other families have a go. :o)