All display entities with blocks (in either block displays or item displays)/custom models (in item display entities) when not precisely aligned with the block grid or otherwise scaled, even in whole numbers, have inconsistent pixel sizes which causes mismatching grids and misalignments.

How to reproduce:

Important: the issue may be hard to see without looking closely, i recommend using a spyglass.
Method 1: block display/item display with a block

1. Use the attached resource pack: display entity inconsistencies test.zip
2. Summon an item display entity or block display entity using either of the following commands:

   /summon item_display 0 64 0 {item:{id:"glowstone"}}

   /summon block_display -0.0 64.5 -0.0 {block_state:{Name:"glowstone"}}

3. Place a block directly adjacent to it.
4. Look closely where the real block and display entity meet.
5. (Optional) Teleport the entity up or down by 0.5 blocks.
   5a. Look closely where the entity and real block meet as you teleport the entity.

Method 2: item display with custom models

1. Use the attached resource pack like above.
2. Summon an item display using the following command:

   /summon item_display 0 64 0 {item:{id:"stick",components:{"minecraft:custom_model_data":1}}}

   This creates a 48x48x48 cube.

3. Build a pillar of glowstone beside the model, and place slabs of any type below the model.
4. Look closely where the model and blocks meet, and where the model and slabs meet.
5. Replace the item with the second model using the following command:

   /item replace entity @n[type=minecraft:item_display] container.0 with stick[minecraft:custom_model_data=2]

   This creates 3 16x16x16 cubes in a pillar.

6. Place blocks adjacent to the pillar.
7. Look closely where the model and blocks meet.
8. Replace the item with the third model using the following command:

   /item replace entity @n[type=minecraft:item_display] container.0 with stick[minecraft:custom_model_data=3]

   This creates 3 16x16x16 cubes with the center cube offset by 4 pixels in two directions.

9. Look closely where the cubes in the model meet.
10. (Optional) Teleport the display entity up or down by 0.5 blocks.
    10a. Look closely at how the alignment changes.

The issue does not require the resource pack but it can make it more obvious.

Observed & expected results:

There are visible misalignments in textures' grids between display entities and real blocks when the entity is not perfectly aligned with the grid, and even between individual parts of custom models. It is expected that block/item display entities would look identical to real blocks when placed next to them even when not in line with the block grid, and that custom models would be aligned regardless of where the elements of the model are placed.

Notes:

Attached are screenshots of my following the steps in the second method, as well as highlighted screenshots showcasing where the misalignments occur. This might not be noticeable to most players but for those of us who try to be precise with custom experiences, it's very discouraging to have all that work go to waste due to simple misalignments in textures.