Unofficial Fallout 4 Patch

I'm guessing there's an engine limitation involved here - the rad chickens and rad rabbits probably have to be set up as enemies for them to run away from the player (due to the combination of AI values and low level and offense/defense values). If they were neutral or better toward the player, they'd just wander around. If you want a mod to test that, there's one called "Henrys All Animals BeFriend for Fallout 4". The description doesn't mention the rad chickens faction, but I checked in FO4Edit, and the mod affects them as well.

I'm not sure how these are handled for sure, but certain animals like deer and elk will appear as enemies in the UI in Skyrim. There's a chance that rad chickens and rad rabbits are handled the same way in FO4 and that's it's either by design or due to a limitation in the engine/UI as mentioned in the comment above.

Don't know if it's by design, but yes, this is due to how they are set up to make them run from the player.