[homeomorphic]

It doesn't matter. He's counting the number of times a continuous curve C on the surface of the Earth crosses other continuous curves (state boundaries). A crossing is a property of the curve and its embedding onto the Earth's surface. While a (continuous) map projection can deform both C and the state boundaries, it cannot create or destroy crossings.

To draw the crossings, however, he needs to pick a projection and project both C and the state boundaries, which I guess is why he included some PROJ.4 calls.

[abstrakraft]

It does matter - he only considers continuous curves that are projected onto straight lines, which is a property of the projection.