Hello.
If You are blind and only You, things to sort in fridge depends on You. So, You have own system and that's It.
But what if You are married? In this case You'll have to have own system and eachother will know about It.

It can be more difficult if one is sighted and the other is blind. Sighted people rarely contain themselves to systems, generally speaking.

Not married, but in a family with 4 other members.
I'm not fully blind but 2% VI, so I can't really identify things in the fridge either. I don't need a lot of things from it so far though, but all the things I get from there such as bottles I can either scan with Seeing AI or identify by how they feel, and some things are also in a fixed location. But it's a good question. It's surely easyer if you have a system/sorting everyone can get used to.

When I lived with my mom, we had a common system in the fridge.
Honestly she invented it for me when I was yet a child.
From then I follow this system, maybe not 100% of time, but i'm so used to it...
I never lived with a sighted people for long time (long enough to have some problems about fridge) but when I lived two times with a blind girlfriend, they always accepted my ordering system and told that it is comfortable and understandable.
Btw, I hate mess in fridges too! My grandparents never care about it (because they don't need to, we don't live together) and when I visit them for several days I always suffer from being unable to find almost anything in their fridge.
The problem is even more: they live in a very small city and most items they have in their fridge are purchased on a local market and not in usual shops. So items may have no stickers and signatures at all and seeing AI cannot help. Even milk can be in a bottle without any paper on it because local monks sell milk when they think that they have too lots of it.