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.
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.
[1] https://thepepperplant.com/shop.html