If your argument is that probability can't exist because if can't have a causal effect on reality maybe you should try to define and use probability as it's usually done - with the understanding that 'having a causal effect on reality' has nothing to do with it.

Probability can be used to say things about reality. 'Things' like 'what we know or expect'. Probability is about uncertainty. Statistical mechanics will say things like 'the average energy in that system is whatever' - this is something about reality. Particle physics will say 'the half-life of that muon is whatever'. That's physics as far as my defition of physics goes.

Can physics - in your view - explain that if you put together a glass of hot water and a glass of cold ethanol you end up with a warm mixture of water and ethanol? That "causality" only exists in a probabilistic sense after all...

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[1] You are in good company. Bruno de Finetti wrote:

“My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this:

PROBABILITY DOES NOT EXIST

The abandonment of superstitious beliefs about the existence of the Phlogiston, the Cosmic Ether, Absolute Space and Time, . . . or Fairies and Witches was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a mis- leading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.”