MC-106133 and MC-138004 have been fixed in 19w09a, now pillagers can shoot tipped arrows and firework rockets from their offhand, but they will be used up.
The command of pillager with poison arrows is

/summon minecraft:pillager ~ ~ ~ {HandItems:[{id:"crossbow",Count:1},{id:"tipped_arrow",Count:1,tag:{Potion:"long_poison"}}]}

The command of pillager with firework rockets is

/summon minecraft:pillager ~ ~ ~ {HandItems:[{id:"crossbow",Count:1},{id:"firework_rocket",Count:1,tag:{Fireworks:{Explosions:[{Type:2,Flicker:1,Colors:[I;3887386,14602026],FadeColors:[I;5320730]}],Flight:3}}}]}

You can change the"Count:1" to more, but the limit is 64

Their tipped arrows or firework rockets are not infinite. After they shoot it for a certain number of times (depends on the "Count" tag in the command), their offhand will be empty and they can only shoot normal arrows.

This issue doesn't happen to skeletons, strays or wither skeletons.