I was working on trying to build a piston door, and the timings were wrong, causing one of the pistons to push its block through the bundled wire connecting the top and bottom of the door, freezing anyone in view range - The world is a LAN and we were building separate bases, my friend hosting the world. I would get frozen, but he would be fine, until he came to help me check out why it was doing this to me, and it froze both of us. He then got on in singleplayer, activated the system, and once again it froze him.

I tested in single player in a superflat and placed a piston to push a block into a bundled cable - if there were no signals going through the wire, it caused no issues, but when I turned on a wire signal and then pushed the block, the game froze. There were only pistons, a stone block, bundled cable (not colored) and white, orange, and magenta insulated wires being ran through the bundled cable, all of which were on.

FoamFix is installed, but there is no Optifine, or Fastcraft.

Not sure what you mean. You can't push a block if there is another block in the way. You also can't push bundled cables with pistons. You also didn't post any kind of crash log or screenshot. Please give me more info. A screenshot of the setup would be helpful.

I believe Quark allows pushing tiles, its entirely possible I broke then fixed something in FMP related to this, but without crash reports we can do nothing.

Closing due to lack of information. Reopen once you can A) confirm if you are using Quark and B) provide crash logs.