I'm new to modding with forge, and I'm trying to figure out how to make a chest that can be moved by pistons. I assume it involves having to make a new abstract block entity class, but I'm not sure how to override the settings that make block entities immovable by pistons. Any help would be appreciated :)

TL;DR, you can't. The piston logic has an explicit check against push block entities.

The only real option to override a BlockEntity's PushReaction is DESTROY which will destroy the block and spawn its drops.

See for example BedBlock.getPistonPushReaction()

 

The issue is Minecraft's piston logic has no code to properly support moving block entities.

e.g. copying the chest's inventory from the start location to a newly created BlockEntity in the end location.

 

I'm pretty sure if they tried to support it, it would probably be a major source of item duping glitches. 🙂 

So now what I'm curious about is how to make a piston variant that can push block entities

 

You could try copying the piston code into a new block along with the supporting classes.

The key changes will be

* making PistonResolverStructure save the NBT from block entities that are to be pushed so it can reapply it to the new block entity.

* remove the check in PistonBaseBlock.isPushable() that stops block entities being pushed.

 

You will probably find that this doesn't work properly. Not just because it is hard to get right, but there likely a lot of hardwired Minecraft code elsewhere that expects the piston to be its specific class/instance?

 

Other issues include (the hard to get right part): 

* How to handle things like vanilla's double chests when you only push part of it?

* pistons trying to push other pistons need special handling. But the vanilla piston won't know how to handle your piston.

Ah thanks