I would say yes because I am very close to understanding it :) Although I have a math teacher degree, we didn't really learn that much higher level stuff and also it's been twenty years since I touched anything like this. Notation wise I am missing A△B and not much else. For the theorems mentioned, I am reasonably sure if I worked through https://www.ihes.fr/~duminil/publi/2017percolation.pdf I would understand this paper in question.

Edit: ah! I paged through the percolation introduction and it mentions A∆B ∶= (B ∖ A) ∪ (A ∖ B) so that's the symmetric difference between A and B. And it seems the first ten pages is enough, we only need to get to the Russo theorem.