obstruct, hinder, block, deter
礙 centers on creating a physical or figurative barrier that stops movement or progress: obstructing, hindering, blocking, or deterring.
礙 combines 石 (stone) with 疑, which likely contributes the sound and the idea of something that stops or blocks, as a stone obstacle would.
A stone 石 on the left and 疑 (which can suggest doubt or hesitation) on the right: imagine a large stone that makes you hesitate, blocking your path.
For ガイ, picture a guy trying to pass but a stone blocks his way: guy -> ガイ, and the stone obstructs him.