In a current campaign, I'm a bard playing alongside a necromancer who has some pretty powerful zombies that from time to time could use some inspiration. The Bardic Inspiration only mentions creatures within 60 ft can be inspired it does not single out anything that cannot get inspired, however giving a zombie inspiration seems counterintuitive especially giving the other features of the undead as the can't be healed under normal means. So can zombies be inspired?
As you point out, the text of Bardic Inspiration does not exclude any creature types, which means that RAW, zombies can be inspired.
This is not weird
The MM entries for zombies explicitly state that zombies can understand the languages that they knew in life. This means that they do have some kind of mental process that could be affected by Bardic Inspiration. Moreover, their INT of 3 makes them slightly smarter than many animals, which can also be inspired.