Condiments are kind of a gray area on carnivore…? Strict carnivore doesn’t allow them as they contain plants but “normal” carnivore, the not super strict ones often uses them. Which ones, that’s probably individual. I am the “worst” but I always called mine carnivore-ISH exactly to allow the tiny and for me, pretty harmless things to get the joy and variety I need.
Mayo… I would allow my yolk, lard, mustard one but not some store-bought thing with who knows what in it. I don’t like not homemade (by me, it’s important) mayo so I am not knowledgeable about them but surely there are better and worse and horrible ones.
And mayo is mostly oil. That’s why I dislike it. My homemade mayo (I don’t need it but made it once) is mostly yolk, I am not sure it can be called mayo… 
So it’s pretty important what kind of oil it is. And what else are the ingredients. Many ketoers and carnivores don’t only focus on what the woe allows but they avoid many items for health reasons. I cut off very nearly all very processed items way before keto. Mustard not made from a few basic ingredients (but NO sugar) only could stay because mustard is so very important for me and my own mustard is so not right.
Soy sauce is OK to me but again, I am pretty indulgent if it’s about condiments. I only use a little when my fried pork has problems (I can’t always buy the right cut and there are differences anyway, maybe I got bored a bit) as it makes it better. Very, very rarely, I am sure it’s fine for me. But it’s not fully allowed in my world as it isn’t carnivore, it’s just for emergencies once in a blue moon. (I go off KETO more often than that anyway…)
I think if these things help, maybe they are crutches in the beginning and you don’t need to do full elimination, use them if you want…?
Sauce with lots of sugar is definitely not okay. I think avoiding sweet things is quite important for many but of course it depends on our goals…
My worst item that I do my best not to use on carnivore (it’s easy as I like to avoid cheese now and I only use that condiment with cheese) is a condiment with sugar. Not much sugar and I use the condiment in tiny amounts but still. I won’t buy that thing again. That’s even worse than my mustard with erythritol (it isn’t sweet, per se… and I wrote about my subpar mustard)…
I am aware of the ingredients and do my best to use the off items as little and infrequent as I comfortably can. It got better with time, my preferences changed.
So I guess we all should figure out for ourselves what we allow. I always was pretty indulgent because I didn’t need something super strict that would have been impossible to follow anyway.
If one can do and may need a full strict version, that’s great. But not my way.