As of Monsters of the Multiverse, Minotaurs have a trait giving them the Humanoid creature type.
Minotaurs were reworked in Mordenkainen Presents: Monsters of the Multiverse. The playable race now has the racial trait:
As a minotaur, you have the following racial traits.
Creature Type. You are a Humanoid.
Which unambiguously clears up the question about hold person and other spells that specifically target humanoids.
While the original minotaur race is obsolete, I will leave the proceeding discussion for its historical value and applicability to the original iteration of the race.
Minotaur player characters are barrel-chested humanoids.
It says it in the introduction to the playable race, and on page 18 of Guildmaster's Guide to Ravnica and page 22 of Mythic Odysseys of Theros:
Minotaurs are barrel-chested humanoids.
So a minotaur is affected by hold person.
As you have observed, the two playable races that are not humanoids are given racial traits that explicit designate them as non-humanoids.
NPCs use statblocks
Interstingly enough, the description of the minotaur in the Monster Manual describes minotaurs like so:
Their fur stained with the blood of fallen foes, minotaurs are massive, bull-headed humanoids
Yet, their creature type is monstrosity. Why? NPCs use statblocks. The introduction to the Monster Manual says:
A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.
One of these statistics is creature type, and a monster's statblock includes all of its creature types.
PCs use playable races
In contrast with NPCs, player characters use the character creation material found in the various sourcebooks of Dungeons and Dragons. In our particular case, we can find the minotaur playable race in Guildmaster's Guide to Ravnica and Mythic Odysseys of Theros. The Races section of Theros says:
This chapter provides information about the following common playable races of Theros, as well as racial traits for all of them except humans.
The traits described in this chapter are the traits used for player characters playing as minotaurs. Consequently, nowhere in this chapter (or the parallel chapter in Ravnica) are Minotaurs described as monstrosities, rather they are explicitly described as humanoids.
Finally, since they lack a racial trait like the Satyr and Centaur that explicitly names their creature type as anything other than humanoid, we conclude that when the book says "Minotaurs are barrel-chested humanoids", it means they are humanoids.
Humanoid is explicitly the default creature type for playable races.
In Chapter 1 of the PHB we see (pg. 11):
Every character belongs to a race, one of the many intelligent humanoid species in the D&D world.
This is found in the Step-by-Step Character Creation chapter of the PHB. Further, we have an important rule to follow, from the Introduction of the PHB (pg. 7):
that said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.
The races which break this general rule about humanoid PCs (Satyr, Centaur) have specific rules which create the exception:
Your creature type is fey, rather than humanoid.
Since we see nothing similar for the Minotaur playable race, we conclude Minotaur PCs are humanoids.
I can discern my PC's creature type without the Monster Manual.
After all of this, we can finally offer this compelling heuristic argument.
Heuristic 1: I don't need the Monster Manual to create my character.
Everything I need to create my player character is found in the Player's Handbook, or if I am using non-PHB player options, whatever the attendant sourcebook is. In our case, if I am playing a Minotaur, I should be able to know everything I need to know about my Minotaur player character by consulting the PHB and either Ravnica or Theros.
Heuristic 2: Ravnica and Theros do not contain NPC statblocks for the Minotaur.
The reason we know that an NPC Minotaur has creature type monstrosity is because it says so in the Monster Manual on its statblock. But Ravnica and Theros do not contain a statblock for the Minotaur.
If I am a new player creating a Minotaur player character using Theros or Ravnica, I will first encounter in the PHB the statement:
Every character belongs to a race, one of the many intelligent humanoid species in the D&D world.
Then, as I go on to read the playable races section of Ravnica or Theros, I will never encounter the word "monstrosity" in relation to Minotaurs, only the statement:
Minotaurs are barrel-chested humanoids.
Minotaurs may be big, hairy, and terrifying. But even Minotaurs are people who want to be held sometimes.
Thomas casts hold person.
