Air carrier First Officer reported a NMAC while on final approach Runway 28L SFO with another commercial carrier on approach to Runway 28R. The reporter stated the other carrier appeared to drift from the 28R flight path towards the FO's flight path and then executed a missed approach.

Narrative

While on visual approach to SFO 28L in night (or nearing night) VFR conditions; at approximately 1000 AGL (I could be incorrect about the exact altitude); an aircraft (Aircraft Y; if I recall correctly) that was on a visual approach to 28R and converging from the right (East) to intercept the straight-in portion of that approach (I assume it was the FMS Bridge Visual 28R) came close enough to our aircraft that it appeared to me that the other aircraft crossed the extended centerline of 28R; encroaching into the area between the extended centerlines of 28R and 28L; and creating what appeared to me to qualify as a near mid-air collision (less than 500 ft. separation; but cannot be certain of that); at which point the crew of that aircraft conducted a missed approach; while we continued our approach to a safe landing. The following events occurred leading up to this situation: As Pilot flying (PF); I was hand flying the entire visual approach from approximately 8000 MSL; at a point well before receiving initial vectors for the visual approach. NORCAL Approach vectored us on to the visual approach to 28L; pointing out traffic on approach to 28R. At some point along the approach we established and reported visual contact with that aircraft. Additionally; NORCAL Approach gave us some airspeed assignments; including a final assigned speed of 160 KTS. We maintained compliance with all ATC instructions throughout the approach; and were cognizant of the close parallel proximity of the aircraft on approach to 28R. The CA (Captain) (PM) and I discussed the importance of remaining on the extended centerline to 28L and not deviating to the right; in order to maintain safe separation from the other aircraft. We noted the crosswind from the left as a factor to consider; and verbalized that we thought that might help the other aircraft not get too close to us. At one point the CA suggested flying left of extended centerline to create an additional margin of safe separation; which I did for a period of time. Realizing that the way ATC had vectored both aircraft; we were not staggered with any significant amount of in-trail distance from each other; and that we seemed to be at similar speeds; we were aware of and discussed the threat of our proximity to each other. I mentioned that I was surprised that ATC had slowed us to 160 KTS (we are often at 180 KTS at that point on the approach) given that that speed contributed to us not being more staggered from each other in-trail on the parallel approaches. I verbalized that I might maintain 160 KTS for longer than I would normally do so; in order to attempt to get further ahead of the other aircraft in an attempt to not end up wingtip to wingtip. I attempted to do so; but with not much significant change in our proximity to the other aircraft; before needing to continue configuring and slowing to final approach speed.At some point (perhaps in the proximity of 1000-1200 MSL?) we received at Traffic Alert (TA). I had the aircraft in sight over my right shoulder; and the CA elected to switch the TCAS from TA/RA to TA Only. I believe that decision was in compliance with FOM TCAS TA/RA Mode usage guidance and the SFO XX-XX page regarding TCAS considerations and the guidance on when it is acceptable to select TA-ONLY. Shortly thereafter; the other aircraft notified SFO Tower that they were going around. I looked over and up at that aircraft as it initiated the go around and I can say that I don't think I ever seen another aircraft that close while airborne; and it appeared to me that it had overflown the intercept to the final approach course to 28R. I don't know if that aircraft had also selected TA-ONLY or if they were responding to an RA. I don't recall them telling ATC they were responding to an RA.