I appreciate that there's already discussion about this - I've effectively given up on a few decks because of this issue.

@Moocow17 @WotC

This does appear to be a design failure, as 205.3h includes Shrine as an enchantment type, however these appear to be the ONLY enchantment creatures that do not have a creature subtype.

Indeed, I believe these are the only creatures without a type in standard. (Nameless Race all the way back in 'The Dark' and facedown Morph creatures being the only other exceptions I can think of).

March of the Machines and Starfield of Nyx could also cause this effect, although they would not cause this specific issue.

Edit:
Reconfigure creatures DO appear to all also have a creature type in addition to the 'Equipment' artifact type.

For anyone who is having this 'issue' (as I just had yesterday with the Reconfigure creatures), I found in the rules that it technically isn't a bug. I personally think it's bad game design, but it's not a bug. The rules actually specify which subtypes are creature types and which are artifact types (or other types).
The governing clause for this is 205.3c:
205.3c If a card with multiple card types has one or more subtypes, each subtype is correlated to its appropriate card type.
Example: Dryad Arbor’s type line says “Land Creature — Forest Dryad.” Forest is a land type, and Dryad is a creature type.
It goes on to explicitly list the subtypes of each card type. Equipment is listed as a subtype of Artifact in 205.3g, but not as a subtype of Creature in 205.3m:
205.3g Artifacts have their own unique set of subtypes; these subtypes are called artifact types. The artifact types are Blood, Clue, Contraption, Equipment (see rule 301.5), Food, Fortification (see rule 301.6), Gold, Powerstone, Treasure, and Vehicle (see rule 301.7).
...
205.3m Creatures and tribals share their lists of subtypes; these subtypes are called creature types. The creature types are Advisor, Aetherborn, Ally, Angel, Antelope, Ape, Archer, Archon, Army, Artificer, Assassin, Assembly-Worker, Atog, Aurochs, Avatar, Azra, Badger, Barbarian, Bard, Basilisk, Bat, Bear, Beast, Beeble, Beholder, Berserker, Bird, Blinkmoth, Boar, Bringer, Brushwagg, Camarid, Camel, Caribou, Carrier, Cat, Centaur, Cephalid, Chimera, Citizen, Cleric, Cockatrice, Construct, Coward, Crab, Crocodile, Cyclops, Dauthi, Demigod, Demon, Deserter, Devil, Dinosaur, Djinn, Dog, Dragon, Drake, Dreadnought, Drone, Druid, Dryad, Dwarf, Efreet, Egg, Elder, Eldrazi, Elemental, Elephant, Elf, Elk, Eye, Faerie, Ferret, Fish...

I was playing in a Quick draft kamigawa neon dynasty. There was a mistake with secluded courtyard. It would not allow me to name Shrine as the creature type.

Shrine is an enchantment type, just like the Reconfigure creatures don't have Equipment as a creature type

so why cant i choose shrine as a creature type for the land secluded courtyard? seems like they included the land in this set to enable 5 color shrines as a draft archetype but once again arena drops the ball

I just lost a game because of this.

I almost lost a game because of it, please fix it asap!

This is a major issue, as I splashed for shrines counting on Courtyard for mana.

I lost a freaking mtg arena game because of this. They have the audacity to charge $25 for entry to a broken game!

Had this problem in game 2 of my current draft. Nearly lost the game as the shrines are my only splash but I'm only running 2-3 off-color sources.

indeed, I drafted a deck with multiple off-color shrines and wanted to fix with courtyard for them, but was unable to.