Summary: If you replace the Pillagers weapon with a weapon other than a bow or a crossbow, the Pillager doesn't do a melee attack like Vindicators and instead shoots like skeletons.

If you replace the skeletons or strays weapon with the crossbow, the skeleton/stray doesn't charge the crossbow and just sits their doing nothing.

How to reproduce (for Pillagers):

1. Summon a Pillager
2. Use the command: /replaceitem entity @e[type=pillager] slot.weapon.mainhand 1 air
3. Have the Pillager shoot a Villager

Observed Result: The Pillager Shoots like a skeleton

Expected Result: The Pillager charges at the enemy like Vindicator do

How to reproduce (for skeletons/strays)

1. Summon a skeleton/stray
2. Use the command:
3. For skeletons: /replaceitem entity @e[type=skeleton] slot.weapon.mainhand 1 crossbow
4. For strays: /replaceitem entity @e[type=stray] slot.weapon.mainhand 1 crossbow
5. Be in survival mode

Observed Result: The skeleton/stray holds the crossbow weirdly

Expected Result: The skeleton/stray uses the crossbow like the Pillagers do

If the Pillager and skeleton/stray issues need to be in separated bug reports, I'm more than happy to do that, I was unsure of that since they're similar.