Hot Sauce is kind of annoying because it lasts so long after the best by dates. Like it could just be kicking around in then fridge for a couple years and not grow anything on it, but it is probably time to toss it out eventually?
Particularly if the sauce includes unstrained organic bits such as garlic or onions, or includes oils - botulism (odorless, tasteless) can be a non-zero risk.
At some point, that crusty $5 bottle of hot sauce you found in the back of the fridge should just get tossed out instead of taking the risk.
Tabasco in particular isn't just vinegar-based, it's nearly entirely vinegar. Its ingredients list is vinegar, salt and crushed peppers that are then strained before bottling. It is a very inhospitable environment for botulism - or anything else.
Many other types of hot sauces contain oils and/or are not strained of organic matter and/or contain blended organic matter. Such as all of your thicker or chunkier sauces for the most part[1] (which happen to be my favorites). Those should be kept in the fridge and you should discard after some time just to be on the safe side.