BE Pillagers don't act like range mob, they pounce in front of the player and face to face shooting. Also they won't focus on target and keep running around when charging its crossbow. Their crossbow enchantment is invalid. (already logged: MCPE-35286)
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Resolving as a duplicate of MCPE-42471.
Also the AI are outdate to Pillagers. In Java it fixed MC-137755 and MC-137977