i always thought yuts!izuku was using a modified sign language—sign language doesn't do discrete or subtle well, there are too many signs that have to be signed on the chest or face. so izuku's using a heavily modified sign language, or tactile signing, and koda's using standard, full-body sign language. they probably wouldn't be able to understand each other!
This is true. In my head, Izuku is used to signing discreetly, or disguising it as nervous hand-wringing, and Rei is used to seeing it that way, so while Izuku’s gestures are easily identified as sign language to someone who knows it, they’re also sort of… garbled, I guess? And since he habitually mutters out loud, it’s easy to assume he does it with sign, too.