C172 Flight Instructor with student reported an NMAC during final approach at a non-towered airport.

Narrative

My student and I were on a short-final doing a practice approach for the ILS XX into ZZZ full-stop. When we were approx. a mile from the runway; a RV formation aircraft did a short-approach base-to-final leg. The RV's course was coming right at us; and the RV was committed to a steep descent and turn in our direction. The pilot of the RV made a radio call of the base-to-final/short-approach leg; and I started scanning for the RV as a result. Our Garmin ADSB-in started chiming as the RV got closer; and we had visual of the aircraft when it was approx. 150 feet away from us. I took controls from my student; made a strong evasive action to pull the plane away from the RV; and did a go-around. The RV also went around; and we maintained visual separation for the rest of the flight with no other instances occurring. I asked the RV what their intentions were and why they cut us off; and the pilot had said they mistook us for an aircraft also on the ILS approx. 2 NM behind us; and did not see us until we were close-distance. The pilot apologized; and any potential accident was avoided.