In CAA world, As long as your field of vision is acceptable, and you pass your single eye acuity, presence of stereoscopsis is not independently tested. Often lack of depth perception occurs due to amblyopia, however this in itself is not disqualifying. Single eye visual acuity criteria will need to be met.
In FAA world, monocularity is not a problem.
In the real world, speaking as some with no depth perception, it's not an issue. the brain learns to interpret the cue available.