Is it possible for the center image to drift from lp to lp?

Is your turntable level? Is the cartridge properly aligned? Are there any issues with the pickup arm leads binding, or any issues with the pickup arm bearings? Is the stylus pristine and clean? Do you have this problem with sources other than LP?

Some details on your system might be helpful.

#3 and #4!

If you listened to the group in person, the singer usually moves around also.

Recordings are not like real life, and maybe the person doing the recording mix was not listening in the center, between the speakers.  Not all vocals are in the center, on every Lp.

The cutting head on the master lathe was installed by hand. It would be nice to think every human installing this head installed it perfectly perpendicular. The act of tightening said head to the lathe was done with screws. yada yada yada.

Your stylus diamond was installed by hand, human hands.

Album thickness means VTA is perfect on some albums, and off on others. etc. etc. etc.

Stop your obsession. Enjoy the music.

Here's something that may make no sense. If you have everything perfectly setup. If you have a really good system. If all the stars are aligned.  What happens when the singer moves their head, this in the middle of a song. Does your system accurately reproduce the now moved center of the singers vocal cords.

Stop your obsession. Enjoy the music.

Mine does this and I have thought of several factors.  Wear of the record, tubes' gain changing, system warmup, differences in tracking different parts of the record, volume control mistracking at various settings.  I have a preamp with separate volume controls so this is rarely a problem I cannot fix but could be annoying with the lack of this.  Getting this right greatly improves my soundstage.

I hear it too, and I vote for 2, 3 and 4. Of course, this may have something to do with the fact that I am 70 (seriously, though, I hear just fine to 11KHz, lab measurement, repeatable). And I have taken care of the obvious things, as CLEEDS suggests.