Good luck getting a definitive answer to this. I have searched and asked and have still not gotten a definitive answer. I think there is a relative unease in giving advice since the wrong advice can lead to illness and worst case, death.
Here's a USDA pamphlet on botulinum:
https://www.fsis.usda.gov/wps/wcm/connect/a70a5447-9490-4855-af0d-e617ea6b5e46/Clostridium_botulinum.pdf?MOD=AJPERES
From the pamphlet: "C. botulinum cannot grow below a pH of 4.6". Given that our home pH testing equipment will not be as accurate as industrial or scientific gear, I aim for a pH below 4 just to be sure.
Now you would imagine that something like ketchup which has a pH below 4 should be shelf stable. But it still has "refrigerate after opening" on the label. So do dill pickles and other stuff which you would imagine are shelf stable even after opening. I think this is more of a CYA thing but if you have a pickle that's floating above the acidic pickling liquid, then it may no longer be acidic and could go off.
Another issue is that our home equipment may not be as sanitary as an industrial facility so we may be introducing bugs into our sauces from our pans, knives, blenders, bottles etc. So use a sanitizer after cleaning your equipment. It ensures you're keeping things as clean as possible.
My personal rules of thumb:
- Keep everything clean and sanitize
- Make sauces below pH 4 and water bath can (boil in the canning jar for 10 mins) sauce I want to keep unrefrigerated
- Pressure can stuff that's above pH 4 following the guidelines provided (e.g. for a pepper/onion mash it was something like 35 mins)
- Refrigerate <pH 4 sauces that I'm not canning