Consecutively setting skeleton's "Fire" data to something prevents it from firing its bow.

1- Summon a skeleton

2- Place a repeating command block with the following command;

^{data modify entity @e[type=minecraft:skeleton,limit=1,sort=nearest] Fire set value -20}

3- Set your gamemode to survival

4- See how the skeleton isn't shooting you even though it's charging up its bow and following you around.

^{Video to reproduce}