R134a is being phased out. There are a few replacements coming out.
Most cars have already switched to R1234yf, (2,3,3,3-Tetrafluoropropene) and the commercial/residential refrigeration market will likely follow. It has an extremely low global warming factor, is very stable, and has beneficial saturation temperature and vapor pressure properties (it's efficient). R1234yf is technically flammable under certain conditions, but nothing that anyone is ever going to see in a kitchen (other than the kitchen already being on fire...rendering the point moot.)
Essentially, 1234yf will burn in a fire, but it does not CATCH on fire any easier than most other things you'll find/use in your life. Your fridge guy is being a big baby.