Computer keeps shutting down after plugging freezer into inverter

Sorry for the late answer--Using a simple relay with NC/NO (normally closed/normally open) contacts and your refrigerator temperature controller.

Basically, connect the AC power (hot) wire to the "common" contact in the relay. Connect the freezer to the NC contact (freezer will run if refrigerator is off). Connect the refrigerator AC power to the NO contact. And you can connect all of the white wire/neutral connections together (only hot lead needs to be switched).

Connect the output of the refrigerator controller to turn on the relay when the refrigerator needs cooling. The relay coil voltage needs to be the value that the controller outputs/will control (120 VAC, 12 VDC, etc.).

Every the refrigerator needs to start, the controller will switch the AC power from the Freezer to the Refrigerator. And you will not have both motors starting/running at once.

You can test the freezer+refrigerator starting at once by cutting the AC power, crank both thermostats to "cold" (so both will turn on when AC power is supplied), then turn on the AC power (use a power string or something) and see what happens. if it reliably starts, then there may not be any issue at all.

-Bill