See summary.

How to reproduce:

1. Spawn a villager, as this is one of the few mobs illagers are hostile to.
2. Put yourself in survival mode.
3. Type in the following command, using "illusioner" or "pillager" instead of "[illager]":

   /summon [illager] ~ ~ ~ {HandItems:[{},{}]}

NOTES:

1. This is NOT the case for Evokers and Vindicators (who normally wield iron axes, and thus use melee attacks no matter what).
2. Villagers still run away from the harmless Pillager. (Not the Illusioner; this is MC-116355)
3. Illusioners still create illusions if the player is nearby. This is the only way for them to reveal their held item if it is not a bow.
4. It seems I'm not the first to discover this bug; a comment on "Can Skeletons Use Crossbows?" by Phoenix SC ( https://www.youtube.com/watch?v=McU0QILC4_o ) states that "Pillagers become passive when they don't have a crossbow, and illusioners become passive when they don't have a bow."