I think this is simply because its old, but whenever the fridge "kicks on", it being on the same circuit as the TV makes the TV turn off/back on. Just curious if there is anything I can do other than a new fridge or getting them off the same circuit (not possible). Any advice appreciated!
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!
Get a Surge & Brown-out power strip, kind of tough to find but that might be enough. Or, do what other people do, which isn't really the safest conditions. Run an extension cord from another outlet on a different circuit. Make sure the run doesn't cross any door ways or traffic areas & rides the wall(s).
Other than that, you could get an electrician & see if the fridge circuit could be refreshed with a new outlet or higher rated one. Which leads to my next point. If this situation hasn't always been present & is fairly recent. Then, an Appliance Repairer might be the real solution. Your compressor motor might be starting to fail & pulling much more power than it should be.