The "caring" interpretation doesn't say that caring is part of reality (except insofar as minds are implemented in reality). Rather, it says that probability isn't part of reality, it's part of decision theory (again except insofar as minds are implemented in reality).

Hmmm - caring as a part of reality? Why not just flip things up, and consider that emotion is also part of reality. Random by any other name. Try to exclude it and you'll find you can't no matter how infinitely many worlds you suppose. There's also calculus to irrationality . . .