Wizards currently allows a hybrid humanoid-monstrosity Race
Unearthed Arcana recently released the Centaur and Minotaur Races for playtest. These races are both listed as:
Hybrid Nature You have two creature types: humanoid and monstrosity. You can be affected by a game effect if it works on either of your creature types.
This suggests that there is an existing playtest precedent for multiple creature types/different creature type than Humanoid. However, as it is playtest only, it is unclear as to whether or not Wizards themselves know if it's balanced or if it introduces complications.
Anything that requires a creature type would be affected
Whether or not you decide something is a 'complication' is likely to be opinion-based, but any spell, effect, or ability that requires a certain creature type will be affected by changing creature types.
Examples of spell effects/abilities that will be impacted by changing type
You have already listed Hold Person and Dominate Person, but there are many other spells and effects that include a creature type requirement in their descriptions. This includes things such as
- Spell Calm Emotions
- Paladin's Divine Smite
- Paladin's Divine Sense
- Warlock's Gaze of Two Minds
There are many more, but whether or not it will cause a complication in your world depends on your specific world, the creatures within it, and the abilities they use and have.