Around what apparent magnitude can the naked eye observe an object during full moon For a very rough guideline using healthy/corrected eyes adjusted to the dark, around how bright should an object be to expect it to be visible?
It may shave off 1 or 2 magnitudes, but it depends on many factors: nature of the object (star, nebula, galaxy), altitude (higher altitude has less light scatter), transparency, etc. There's no One Single Answer To Rule Them All.

Light pollution from artificial sources has a greater impact in most cases.