Fridge starting up turns TV on/off
Your cheapest option besides a new fridge might be a UPS for the TV.

Make sure you get at least a line interactive type. The offline / standby versions will just pass the dropout spike through to the TV. https://en.m.wikipedia.org/wiki/Uninterruptible_power_supply#Line-interactive

My neighborhood power had some lines rubbing together when it was windy. The power would drop just for an instant but long enough to reset my TiVo causing a 5 minute dropout in any program I was recording. I got a UPS for it and solved the problem until the power company fixed the lines. 

Electronics are sensitive to even the shortest drop in power. A UPS could smooth out the spikes and let your TV ride through the dropouts.
Good luck!