It most likely does not effect worn or carried items, normally
This explanation will rely on two creatures that have a similar mechanic to the green slime: The Rust Monster, and Black Pudding.
Both the Rust Monster and Black Pudding are creatures that can harm equipment. The Rust Monster’s antennae attack will slowly damage WORN or CARRIED armor at a slow but steady rate, and the Black Pudding also damages weapons (that hit it) and armor that is WORN.
What this answer relies on this is the steady and consistent use of ‘Worn’ and ‘Carried’ when deciding these effects. The Green Slime Hazard mentions the one instance that wood or metal items are damaged, when objects made of these materials are used to scrape off the slime.
Rules as Intended….maybe?
The issue I see with going with the interpretation of ‘It effects ANYTHING you are carrying’ is that it DESTROYS metal and wooden objects. Rust Monster/Black Pudding merely damage them, this is an outright removal of an important item. As a hazard that does 1d10 damage for stepping in it, it seems harsh.
It also starts raising a bunch of questions that the game doesn’t normally handle. If I step in it with my left boot, metal, does it ruin my whole armor? What if my right metal glove touches it? Etc.
I believe that the RAW (Rules as Written) of the matter is that the slime would not destroy your armor, and that it shouldn’t for these reasons.
If this thing ruins an immersive experience, just keep in mind in this game you can take a fireball to the face and have your cloth clothes intact. I suggest just imagining you ‘scraped it off really fast’ if it bothers you.