Is there some way to measure mains voltage with the ACS712 sensor?
One thing I saw there is that they were measuring the mains voltage with the ACS712 sensor


No, they weren't using that sensor to measure the mains voltage. It measures current only.


  (as its values had some 0.1V to 0.5V variance when I was talking to them)


That variation in the reported mains voltage does not mean that it was being measured using an ACS712 sensor.


  I couldn't find a way to measure the mains voltage with it


You couldn't find a way to do that, because there isn't a way to do that.

The "live side" measurement connections of the ACS712 (pins 1+2 and 3+4) are isolated from the Hall-effect sensor on the low-voltage side of the device (2.1kV RMS minimum isolation). Therefore the ACS712 cannot be used to measure the "live side" (e.g. mains) voltage.



(Image from ACS712 datasheet)

In summary: The ACS712 + Arduino system which you saw, measured the mains voltage some other way. The ACS712 was used only for the current measurement.