You are very correct and these twitter conversations are the ones I mentioned above recapitulating old Fisher vs Neyman debates, which contradicts the claim that 20th statistics was supposedly causally blind.
In contemporary terms, Neyman was focused on estimating the average treatment effect (ATE) in a randomized controlled trial (RCT). This can be zero even when some or all patient-level treatment effects differ from zero. Because of this he was interested in the long-run operating characteristics of statistical procedures under both random sampling and random allocation, which we discussed here. This is very unrealistic and that is why we essentially never use it in practice, at least not in medicine.
Fisher on the other hand did not care about the ATE and instead focused on a form of abductive inference from RCTs assuming only random allocation and not random sampling. He accordingly tested the sharp null hypothesis that the effect is zero for every single unit. This assumes it is unrealistic to expect that there is benefit for one subgroup and detriment to another with both equalizing to zero.
@Stephen, an applied statistician with tons of experience and thus closer to the Fisherian practical view, summed this up here as: 'Fisher’s null hypothesis can be described as being, “all treatments are equal”, whereas Neyman’s is, “on average all treatments are equal”.’ The ATE framework can also violate Nelder’s marginality principles, which may be one conceptual source of disagreement behind the Lord’s paradox debates with Pearl.
In the contemporary causal inference world, these considerations are well summarized, e.g., by Guido Imbens and Donald Rubin here.
This disconnect between theory and practice can yield endless debates, which can be quite fruitful and useful to follow albeit exhausting for participants.