I noticed that all consumable items can be traded during a game and remain non-muted. But, I was surprised to find that ring of regeneration was also non-muted when I traded it.
What items can be transferred between heroes and not be muted?
All consumables can be shared and used by teammates:
Additionally, basic regeneration items can be shared:
Gem can also be shared. Bottle and Divine Rapier have some interesting rules about sharing that don't come up much: you can't pass off bottled runes, but you can pass a Bottle and your teammate can fill it with a rune, then use it. Divine Rapiers can only be shared if an ally dies and a teammate picks it up, in which case it can be shared only with the original owner.
Besides, like you said, all consumables (wards, courier, tangos, clarities...) can be traded.
The few exceptions to the rule are ring of regeneration, ring of health, sage's mask, void stone, and perseverance. the logic, I've inferred, being:
also, bottles that have a rune in them can't be shared. otherwise, with 0 to 3 charges, they can be given to and used by allies (or enemies!).