In Magic: the Gathering, creature types mostly started as a kind of flavor thing - the Old Man of the Sea from Arabian Nights (the game's first expansion, based on the real-world folktales from the Middle East) had the type-line "Summon Marid," which told you that this was actually some non-human monster, not just a spindly old man. Over the course of the game's evolution, creature types have become a much more regulated thing, eventually seeing a massive errata to older cards to introduce, for example, the "human" creature type, and also to create a convention of humanoid races having a "race" and a "class" creature type - something that might have previously been "summon knight" now said "creature - human knight." These creature types don't have any inherent rules (once they introduced the keyword "defender" that took the "can't attack" element out of the "wall" creature type and when they shifted "legendary" to be a supertype that replaced the old "legend" creature type) but they allow particular cards to care about those types - your Goblin King gets to buff any creatures with the Goblin creature type.
In D&D, there are types that serve a similar function: fiends are creatures that come from the lower planes, undead are any creatures that used to be alive but are now in some sort of living-death (whether they're ghosts or zombies, etc.) and beasts represent animals that are not inherently magical, but are just part of the natural world but don't have the sophisticated intelligence to have a culture or society as we'd recognize it.
Humanoid, then, is the default creature type for playable races. There are a handful of exceptions - Centaurs and Satyrs, who were introduced in D&D's forays into MTG settings, are Fey rather than Humanoid.
But there are some places where this distinction seems a bit odd. For example, probably the most iconic race from Eberron is the Warforged, which are artificial people who are made of metal, wood, and leather, but granted full intelligence, sentience and a soul. In a lot of ways, the story of the Warforged in Eberron is their need to convince the other peoples of the world of their own humanity, and the justified-if-taking-things-too-far machinations of Warforged separatist leader, the Lord of Blades is an example of one person who is fighting back against the other races that have denied them for so long.
Humanoid, thus, makes sense as a kind of declaration by the game that yes, these people are really people, even if they were created in a forge rather than born. But they are very Construct-like humanoids. However, prior to the latest Unearthed Arcana, no creature could have more than one type. (We can get to non-player creatures too - Dracoliches, for example.)
Mechanically, though, it also makes sense to have them as humanoids, given that many healing spells like Cure Wounds don't work on Constructs or Undead. It would be a major penalty for a player character to be unable to receive that sort of healing.
So while the way that it's actually worded would suggest, to me, that having either of those types would disqualify you, the wording of the rules for multiple creature types in the UA article explicitly declare that a creature of both creature types can benefit as if it were either of them - in other words, yes, Cure Wound can't work on a Construct, but if a being is both a Construct and a Humanoid, Cure Wounds can work on them because it works on humanoids (another way to think of it is that it's not that it doesn't work on undead and constructs, but that it works on all creatures other than undead and constructs. If you're humanoid and construct, it means you are a creature type other than constructs or undead.)
Given this, I think we could play around with various races and their creature types.
How far to go with this, is, I think a question of balance and lore, but going through all the official 5e races, let's consider what we have to work with (note, I'm going to cover "bestial races" after the rest.)
PHB:
Tieflings could be both Fiend and Humanoid, which would also create the possibility for good-aligned fiends (if we have evil-aligned celestials, surely the opposite could exist.)
Dragonborn could be both Humanoids and Dragon.
Elemental Evil Player's Companion:
Genasi could be Elemental and Humanoid.
Goliaths could be Giant and Humanoid (consider that in Norse myth, the Jotuns were not always explicitly that large.)
Volo's:
Aasimar could be both Humanoid and Celestial
Mordenkainen:
Some elf subraces (or maybe all elves?) could be Fey and Humanoid
Guildmaster's Guide to Ravnica:
Perhaps Centaurs could be both Fey and Humanoid (though it's odd to me that they're Fey when in the Monster Manual, Centaurs are considered Monstrosities.)
Minotaurs could be Humanoids and Monstrosities.
Mythic Odysseys of Theros:
Like Centaurs, perhaps Satyrs could get the Humanoid tag along with the Fey one.
Eberron: Rising from the Last War:
Warforged, naturally, could be Constructs and Humanoids.
Kalashtar might even be both Aberrations and Humanoids (while they're not merged with the evil, nightmare quori, they are merged with dream-beings, and we know that there are some good-aligned aberrations, like Flumphs).
Changelings could be Humanoid and Monstrosity, to link up with the MM's Doppelgangers.
Now, the big category is Beast-like humanoids. This would include Tortles, Aarakocra, Kenku, Tabaxi, Lizardfolk, Leonin, Loxodons, and possibly Shifters (though they're a bit different). Arguably, Minotaurs could fit here as well, though their status as a classical Greek monster sort of put them more in the Monstrosity side of things, as I see it.
I think this last one (again, maybe not counting Shifters) is a bit tricky. For instance, while you and I would see an Aarakocra or a Kenku as a "bird-person," just seeing avian features on a humanoid body, I could imagine that they would look at humans, elves, dwarves, and halflings and think of us as "ape-people," as that's technically what we are.
Indeed, the distinction between Beast and Humanoid is a particularly tricky one, as on a biological level, the humans upon which "humanoid" is based are, after all, just particularly smart apes. So, I'd be tempted to actually step back from this one and say that even if they have animal-like features, the various "beast-men" races are still, fundamentally, humanoids. Indeed, it might be that the very fact that they exhibit humanoid traits that makes them not beasts. (Let's also consider that some of these changes are intended to remedy ingrained racism within D&D's use of race as a game mechanic, and historically, classifying a group of people as "beasts" or "animals" has been, you know, a tactic to dehumanize them.)
I'd also allow that the use of hybrid creature types in these Gothic Lineages is meant to evoke the horror of being trapped between two realities - that the identity crisis of a Dhampir or Reborn, for instance, is central to their character, while the Warforged are fighting to be recognized as full humanoids in their setting.
But it does raise some interesting possibilities for the future of the game that I'd like to explore.