I've been having luck brewing kombucha this past year and am interested in trying out ginger beer since I have been lead to believe the processes are quite similar (besides the 1 way valve for 1F). Whenever I've brewed kombucha I've stopped 2F after 3-5 days simply by putting the bottles in the fridge. However, I've read a few instructionals on ginger beer that recommend pasteurizing. Is there a difference with a ginger beer bacterial culture (vs a SCOBY for reference) that would cause it to continue fermenting substantially at fridge temperatures?
From what I can tell, the reason people pasteurize ginger beer is to stop fermentation before it is done- not even primary. They might only want enough fermentation to add carbonation, or they want a sweet, low-alcohol final product.
For anything fully fermented with yeast, pasteurization is considered a destructive process, driving off delicate aromatic compounds.
It is possible that someone making a fully-fermented product might want to pasteurize if they put whole pieces of fruit/ginger inside the bottles, and they don't want yeast to slowly find more sugars inside the fruit and create more pressure than the bottle can handle.
If none of the above applies to you, there is no strong reason to pasteurize. It's generally accepted that a sealed beverage fully fermented by yeast is not vulnerable to spoilage at any temperature, let alone in a fridge.
I put fresh kegs of ginger mead in the fridge and they clear nicely.