It would be more correct to say that homeopathy became explicitly based on water memory after atomic theory and the size of atoms achieved mainstream acceptance

It would be more correct to say that homeopathy became explicitly based on water memory after atomic theory and the size of atoms achieved mainstream acceptance. And while Dalton and Avogadro had certainly made convincing arguments based on chemistry in the early 19th century, and thermodynamicists like Boltzman had models of heat and heat transfer that seemed to depend on particles, it wasn't until after Einstein's paper on Brownian motion and Rutherford's interpretation of the Geiger-Marsden experiment that homeopathic dilution just being dilution became an unsustainable notion. It was always a silly notion, especially when numbers like 30C - a dilution of one part in 10^60, or one molecule of the target substance in 3 × 10^34kg of water, after you understand what molecules are - were being thrown around, but there was at least a plausible explanation before, say, WW1.