Mob that avoids any mob with a certain potion effect

Only possible with AI related Manipulation.

Check the Plugins Page. There are Plugins that are really helpful, also I think there was a Plugin that adds some AI related Procedure Blocks.

This doesn't exactly make mobs avoid the afflicted entity, but it does keep them a certain distance away from them.

I thought about the interdiction torches from the Equivalent Exchange/Project E mods and set up a procedure to behave similarly.

This procedure runs on the status effect's "On effect active tick", and it checks for nearby entities without the effect and overrides their velocity on specific axes to prevent them from moving too close to the entity with the effect.

Depending on how exactly you want the effect to function, you may want to check for- and include or exclude specific types of entities.