Despite a bow and arrow being the default weapon of an illusioner and only being able to use that weapon, they will replace their bow with crossbows. The illusioner cannot use the crossbow, so it should not prefer to take that item like other 'illager' type mobs.

One note is that if you give the illusioner a bow, they will pick it up and not take an item like a cross bow after.

Steps to Reproduce:

1. Summon the mob with command

   /summon illusioner ~ ~ ~ {CanPickUpLoot:1b}
   

2. Drop crossbow, they pick it up
3. Drop bow, they do not pick it up