The monarchy in Britain is basically by consent these days, and has held its position since the abdication of Edward VIII in the 30s on the basis of a very effective PR operation. That's why Andrew was stood down from public appearances some time ago: it doesn't matter if he's guilty or not, anything publicly associating the monarchy with child abuse is a public relations disaster.
My personal hope is that Charles is a bad monarch, and William turns out to be one too. That would probably be enough to get us a (ceremonial) presidency on the Irish or Israeli model.