Version 1.1.10

• Minecraft 1.21.1
• Item Collectors

The Item Collector & its upgrade keep adding the NBT tag "custom_data={picked: 1b}
It won't allow items with that tag to be put into the same stack at the same item without that tag.

Use the Advanced Item Collector

Ah the tag appears on the items picked up by the collectors? I assumed you meant the tag appeared on the item collector item.
The entire mod does not contain any 'picked' tag and also does not interact with the tags on picked up items at all.

Mobs get killed & the items are picked up by the Advanced Item Collector. I'm using the mod with the mod pack ATM10. It's been a known issue within the mod pack that your item collectors keep randomly adding that particular NBT tag.

The setup goes like this.

mobs get slain by mob crusher from (Mob Grinding Utils)
items get picked up by AIC (Advanced Item Collector) (its connected directly to ender chest.
Items get pumped into either an enchantment extractor or drawers (industrial foregoing & functional storage respectively).
The NBT tag only appears randomly when using the Advanced Item Collector to grab the items. It's also the quickest item Collector I have at my disposal.

The items ONLY interact with the AIC in a manner that could be used to add a NBT tag.

Unfortunately they are still getting added via your mod, there's no other mod that technically interacts with these items before your item collector

This mod adds no such tag. When does the tag get added?
Might be some other mod you have that's adding that tag.

I was looking through the All The Mods discord and it seems All The Mods now mentions this issue is caused by Let Me Despawn in their latest changelog.
And indeed, it seems Let Me Despawn is adding the 'picked' tag to mobs' items.
https://github.com/frikinjay/let-me-despawn/blob/711b97d149a74e618dd2d2cf41cabab4937a05e5/common/src/main/java/com/frikinjay/letmedespawn/LetMeDespawn.java#L44

This issue seems unrelated to Item Collectors as the collectors just pick up items and do not interact with their custom nbt tag.
Please report the issue to Let Me Despawn.