Good initiative to clean up the wiki on this, I agree it’s very confusing.
Short answer: The Shapeoko is a CNC mill, climb-cut everything.
On manual milling machines, climb-cutting is difficult or even dangerous, because the cutting forces have large components in the positive feed direction, meaning the feed table is pulled into the cutter. That can be pretty difficult to control with a hand-wheel, sort of like using the wrong side on a table router (zwhoosh!).
That’s not an issue on a CNC, obviously, but may be a reason why you still hear advice to use conventional cuts. Or why they are called conventional in the first place.
In real wood, conventional cutting parallel to the grain causes sizeable splinters to come off in one piece, because the cutter acts more or less like a wedge that tries to split the grain.
In metal, starting the cut with the thicker chip (i.e. climbing) is beneficial (see the other thread). Also, carbide tools much prefer the higher compressive loads when the edge hits the stock in a climb cut, as opposed to the tensile loads that occur on exit in conventional cutting. Tungsten carbide and the ceramic friends are much stronger in compression than tension.
Of course, there’s no reason not to try conventional, but I’d vote against recommending it as default in a wiki.