Are there any acrobatic-category aircraft that are also type-certificated/rated and equipped for flight under the instrument flight rules? What limitations would be placed on such an airplane when flying as an IFR aircraft vs. a VFR aircraft?
Communication and navigation equipment VFR DAY, VFR NIGHT OR IFR according to actual requirements of the customers
There would be no particular limitation on operations specifically because the aircraft is capable of aerobatics, but the pilot would still need to follow their clearance. This would significantly limit the benefit of the instrument certification. (Note that even if deviations in altitude and flight path were approved, aerobatics still wouldn't really be possible.)
Most combat trainers are equipped and rated for IFR. For example, Pilatus makes the PC-21!.