Interesting question. I think this might differ from facility to facility.
Where I've worked, we allow IFR aircraft to enter active MOAs, with restrictions to the IFR aircraft or the military aircraft. Sure we'd like you to stay clear, but it never hurts to ask. Some MOAs have transition or “safe” altitudes and/or “corridors”, you’ll just have to ask. Like I said, we can also restrict the military aircraft in the MOA. We prefer not to, but sometimes we have too. We’ll have the military aircraft remain below or above your altitude, have them remain east, west, etc. of your course, restrict their operating area.
With VFR on Top, standard IFR separation is not applied, but controllers are still required to provide you with traffic advisories and safety alerts and apply merging target procedures. The pilot is responsible to comply with visibility and cloud restrictions and be "vigilant so as to see and avoid other aircraft." The pilot is also still responsible to adhere to ATC clearances (FAAO 7110.65 7-3-1).
However, (again, depending on the facility) we still have to keep the aircraft in the MOA separated from you, 3/5 miles 1,000 feet.
Generally speaking, if you have to deviate for weather, the military aircraft probably won't be near it either. Cloudy days mean lower MOA ops for us!
Hope this helps.