Play as any entity you want. Just replace "zombie" with the entity you want. Such as "iron_golem", "wither", and they won't move because they all have No AI.
How to make this mechanism work:
1. Enter "/tp @e[name=follow] (Player's Name)" into a repeat, always active command block.
2. Copy and Paste the command below into the chat bar (or command block, either way is fine)
3. Apply invisibility to your character, through command or potion.
4. Enjoy running around as an entity!