It isn't the same principle. Firstly, coastlines are more jagged because they are hit by waves perpendicularly, while rivers are shaped by water flowing along the banks, smoothing them. Secondly, the borders are typically defined by either the thalweg (greatest depth) or median line, either being smoother lines than the banks. Thirdly, river borders are then in practice defined by measuring the coordinates of particular sample points along the idealized line and then using straight lines or simple mathematical curves to connect these, forming a simple non-fractal boundary.

You could say the exact same set of objections to shoreline paradox.

But most borders are not defined as "on the shoreline", they are defined using something reliable.

Exactly. The coastline paradox is a mathematical curiousity, not a practical objection to measuring things. Coastlines are not infinite length in practice. You define a system of measurement then a length in that system

What? Neither of those three applies to a shoreline.

Physical shorelines instantiations of a true fractal are always limited. I'd go so far as to say that there is no such real object in the world.

I think I'm in agreement with you, but not sure if I'm agreeing that the are no fractals in the world, or that there are no shorelines.

Anyway, true fractal shorelines definitely never put sugar on their porridge.