Can any meaningful optical ground-based observations of deep space objects be made when the moon in any phase is in the night sky?
*Some* objects can be observed even when the moon is in the sky and full. Typically, available observing time is divided up into times when the moon is bright, and times when the moon is either not in the sky, or in a phase where it's not very bright. Certain objects can only be observed during the "dark time" when the moon is not up, so you have to schedule those observing sessions accordingly.
The brightness of your source is what determines whether you need dark time or not. If your source is really dim, then you need dark time. If your source is bright, then you don't. If you have a very extended source, then the moon might also be a problem because it illuminates different parts of the sky by different amounts. But it may be possible to correct for that.
This page was last updated November 21, 2015.