Every time I add gas, engine shuts off

This sounds like a stuck open purge solenoid. When they stick open the fuel vapors from the refueling process get dumped into the engine uncontrolled and it will basically act to flood the cylinders, just like on an older car with a stuck choke. It is a simple part, basically a solenoid the opens to allow the engine to draw off the fuel vapors that build up in the charcoal canister. It is in the rear of the engine compartment on the drivers side. To get to it you need to remove the air box and resonator on that side, then the solenoid is clipped to a bracket near the firewall. It has 2 hoses and an electrical connector on it. Remove the connector, the hoses and remove it from the bracket. The process is reversed to install the replacement. You can test them but I generally find that once they start binding it will happen again and get worse. Oh and FYI in most places it's a bad idea to fuel up with the engine running, if not illegal. That said this sounds like the issue.