You won't have to worry about that. UI on only one eye would be a very bad idea for everyone. I can speculate about someone using it for an intentionally weird and distracting ghost effect or to approximate "impossible colors" like red-and-blue-not-purple. But, otherwise it won't be done.

Also, people with monocular vision have reported that the 3D-ness and presence of VR headsets works just as well as real life. In fact, it's fairly common for people with stereo vision to have a hard time noticing when they are running VR software that intentionally/unintentionally displays in mono.