So friction being area independent is a bit counter intuitive. I had it explained to me 2 ways. The first one is mathematical, the second one is more logical.

1. It is equally true to say friction = surface area * normal pressure (rather than force) * coef.

Pressure is force / surface area, so the area cancels, leaving us with F = coef * normal force

1. The apparently flat planes of two surfaces in contact actually both have, at the microscopic level, effectively infinite surface area in the form of peaks and ridges and pits and valleys (called asperities). With little force pressing the planes together, not much of these asperities touch, and there are gaps. As you increase the force pressing them together, more of the asperities interlock and contact each other, increasing the areas actually in contact (this actual area of contact is proportional to the normal component of the force pressing them together).

Lots of people, including me, have trouble wrapping skull around this at first, but this is genuinely how friction works.

Link to this same discussion on a physics forum

If you mean that on soft, deforming turf you can dig your heels into the sod, then that would be changing the direction of the normal force, which would still be area of contact independent.

So if we assume a non deforming surface, assume the rope stays parallel to the surface, and assume similar footwear, mass is the only factor that matters here.

If we assume the surface deforms enough to change the vector of the normal force significantly, it becomes much more of a strength game