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?
Wikipedia's page on the Bortle Scale claims the full moon at a dark site is roughly equivalent to the light pollution at the urban/suburban transition which means you could see stars with an naked-eye limiting magnitude (NELM) 4.6-5.0
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.