First three categories can crossbreed but it's highly against the rules and has never happened. If it were to happen, any offspring from "divine humanoid" would be a demigod.
A few are god vessels, but they are categorized by traits that all members of their species have. Shulk is a homs, a humanoid that needs a substance called ether to survive, and if he doesn't take special vitamins while in the Smash hub he gets extremely sick, this is why he's "altered humanoid", not his status as a god vessel. Robin is also a god vessel, but a basic humanoid and is thus categorized as such.
Inkling is not with the other humanoids for the following reasons. Inklings have skeletons made of cartilage, not bone, and reproduce by laying eggs that must be kept moist. Internal fertilization happens, then the female deposits the clutch in water, waits a few months, then BABIES. Baby inklings are affectionately called "squishies". Zoras also reproduce this way. Neither can crossbreed with other humanoids.
Feel free to comment and add more headcanons. Mods can move this to FFTF if it's not deemed serious enough.
NOW EDITED TO INCLUDE ALL AVAILABLE CHARACTERS AS OF 1/8/2019