"Creature Type" is a larger restriction than "Race"
I know you didn't want "it's up to the DM" answers, and only wanted RAW. Unfortunately, I'm afraid that "it's up to the DM" is the RAW answer. I'll explain:
The Use Magic Item rules state that (PHB, p. 97):
You ignore all class, race, and level requirements on the use of magic items.
But how do we define race? In standard English, the concept of Race is defined as distinct from species: but the rules contradicts this almost immediately. The concept of race is defined in the Player's handbook (PHB, p. 11):
Every character belongs to a race, one of the many intelligent
humanoid species in the D&D world.
So although the concept of "race" has a common usage in English, for the purposes of the rules, it is a subset of a Creature Type (in this example, humanoid). For example, Goblin and Elf are different races of the Creature Type humanoid.
Type vs. Race
Creature Type is defined in the Monster Manual, as a concept that supercedes all other details of its nature (MM, p. 6):
A monster's type speaks to its fundamental nature. Certain spells, magic items, class features, and other effects in the game interact in special ways with creatures of a particular type.
Right after this, it discusses creatures more specific "tags":
A monster might have one or more tags appended to its type, in parentheses. For example, an orc has the (orc) type. The parenthetical tags provide additional categorization for certain creatures.
We can also see that these tags are places where a creature's race can be defined. This is made explicit on pages 342-350 of the Monster Manual, where every NPC is defined as having type "humanoid (any race)". From this, we see that creature type is more than race: it is a distinction that overrides things which ignore racial restrictions.
So if a centaur isn't humanoid, what is it?
A centaur's Creature Type is listed in the Monster Manaual (p. 38) as Monstrosity. You could argue that a centaur rogue could use a magical device intended for a non-centaur Monstrosity (such as a special saddle designed for a chimera), because the difference between two monstrosities could be seen as a distinction of race. But what stops centaurs from using humanoid leggings is not just that they are different races, it is that they are different creature types altogether.
Fortunately, the Dungeon Master's Guide has explicit instructions on what to do when a nonhumanoid attempts to use humanoid equipment (DMG, p. 141):
When a nonhumanoid tries to wear an item, use your discretion as to whether the item functions as intended. A ring placed on a tentacle might work, but a yuan-ti with a snakelike tail instead of legs can't wear boots.
Since this is in the Dungeon Master's Guide, the "you" in the first sentence of the previous quote refers to the DM. So I'm afraid that in this case, "it's up to the DM" is explicitly RAW.
NOTE: This conversation might be more complicated if we were talking about the Unearthed Arcana Centaur, which has a trait "Hybrid Nature," which explicitly states that its type is both humanoid and monstrosity for the purpose of game effects that works on either. But for this specific homebrew, the RAW stands.