If the raison d'etre for your rule, wealth and power is entirely based on ancestry versus merit, of course all the members of this rareified group will ultimately be protected by the others in it - because the minute people start saying let's throw out this one because he sucks, the public will start examining the entire set up and everyone in it to see who should be tossed next.
The BRF already used up that move with Andrew - notice how much they hated doing it, and let me assure you it wasn't because they love Andy so much - tossing Harry out will allow public opinion to dictate who is royal and who is not and that will be the end of them.
The Divine Right is still in play here, and Harry (and the kids if they are his, but not Meghan) will be covered under that umbrella until the current king passes.
Harry's constant insistance that his genetics make him more important and deserving of special treatment by "ordinary" people and the law is not something he just pulled out of his ass. He's been told this since he was very little and it's shaped how his otherwise unremarkable brain works. He's just saying the quiet part out loud - but every single member of the royal family believes this to their core.
By protecting Harry they are protecting the increasingly shaky ground the entire institution rests on.