Air carrier Captain reported executing a go-around at ORD after experiencing autoflight anomalies possibly related to 5G interference.

Narrative

We were set to execute the ILS 28C which is what the ATIS was reporting. After contacting Chicago Approach; they informed us to expect the RNAV (GPS) 27R. We updated the FMS with RNAV 27R and briefed the approach. VOR updating was turned off. While on Radar vectors; we were given Direct Welev to join the Final for 27R. After joining the final; I notice that my LNAV was indicated full left defection. The VNAV was full up defection; which would be normal since we were below the crossing altitude.At this point; I heard ATC questioning the aircraft ahead of us about their tracking. I took a look at [the] First Officer indication and saw no LNAV/VNAV indication. We both were baffled and could not figure it out. While discussing the matter with FO; aircraft ahead of us did a go around. Shortly after that; we did the same and requested the ILS 28C. Rest of the flight was uneventful; ILS 28C was executed with no issues. After further discussion with FO; we determined that we were perfectly setup for the RNAV 27R approach. Not only did the aircraft ahead of us go around; but so did the aircraft behind us. ATC called me to ask what occurred. I told them what is on this report. They were not sure as to the problem with this approach. ATC controller asked if I thought this was related to 5G. I told him that I did not know.