What is the strongest known RSW result in planar percolation?

This paper of Grimmett and Manolescu prove RSW for bond percolation on isoradial graphs with critical weights (see also this one). The critical weights are those for which the model satisfies the star-triangle relation, and they use this relation, essentially, to transform the graph into a regular grid.

Tassion recently proved the RSW bound for a large class of percolation models including Voronoi percolation, improving upon a weaker result of Bolobás and Riordan.

Then, of course, there's work on RSW for dependent percolation models (FK-percolation, nodal sets of Gaussian random fields).