Citation X (C750)
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness; Confusion
Conflict Airborne Conflict; Inflight Event / Encounter Unstabilized Approach
Air Traffic Control Separated Traffic; Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Executed Go Around / Missed Approach; General Flight Cancelled / Delayed
Airspace Structure; Human Factors; Procedure
We were given an ILS clearance into ZZZ in VMC conditions. A VFR airplane was at our altitude and seemed to be tracking to cross the final approach course. We both had the aircraft in sight and changed to a visual approach to maneuver behind the aircraft. At that point the airplane made a sharp right turn and we had to turn further right (away from the final approach course) to maintain separation. It seemed like the plane was on a long final for ZZZ1 and we were then at 90 degrees off of the final approach and unable to make a stable approach into ZZZ. We called the go-around with Tower and were given a heading and altitude toward the east before switching to Approach Control to come back and try it again.The main issue was the VFR traffic no one was communicating with. The crew did not fully brief the location and potential for conflicting traffic for ZZZ1 when approaching from the south. Had the crew not changed to a visual approach and been given ATC vectors; we may not have had the same issues. A go-around may not have been avoidable due to conflicting traffic but a more thorough brief of the airspace and threats may have increased situational awareness and avoided confusion. We should also have not changed the type of approach at the last minute.
We were given a heading to intercept the localizer to Runway XXL and given a traffic call that was not on frequency. Controller then had us maintain heading and fly through the localizer to avoid traffic which was about 500 ft. above; crossing our path and that of the localizer track. We decided as a crew that if they gave us clearance for the visual; we could maintain separation from the aircraft into ZZZ. We were given just that and made the right turn back towards the runway and began to descend for landing. The general aviation aircraft ahead of us descended into our path and made an unexpected turn as we were continuing. I disconnected the autopilot and continued the turn towards the east to avoid ZZZ3 airspace and aircraft. Once clear of the aircraft; we elected to scrap the approach and were given vectors for another uneventful approach. We were originally on a 5 mile final to Runway XYR when ZZZ swapped runway configuration and we were then rerouted to the south to land north. We briefed the new approach and had the approach loaded and armed. With the change of runways; perhaps there was not enough time to fully brief the new approach and surroundings to point out a runway to the east that could cause some confusion. Some cumulative fatigue was present; as well as it being our third of four legs for the day added to the stress of the situation. I do think the spacing given into ZZZ was a partial factor with a GA aircraft that wasn't talking to anyone. There are steps to help mitigate issues like this; like ensuring complete situational awareness of self and the possibility of others; but ultimately there might always be general aviation aircraft out there operating around controlled airspace's not on frequency.
Flight crew reported a GA aircraft flew through their approach path necessitating a go-around and re-vectoring for the approach.