I won't opt out, but have to say an automatic opt in makes me feel queasy.
It would sit better with me if they gave you multiple opportunities to opt in - eg at the GP, dentist, optician, I think they already do when you get a driving licence, passport application/renewal, when you register at a new house for council tax, that sort of thing.
And then it should be binding, so family members can't veto it. That appears to be the biggest problem.
But just assuming the state can harvest your organs - I am not sure. Obviously if I were desperate for an organ myself or for a loved one, I might feel differently.