One step at a time...
If your car is very modified and the suspension is lowered of track duty, we do alignments with the drivers weight in the seat and a 1/2 a tank of fuel.
"Normal" BMW alignments do not need the driver in the seat. The engineers know this and the specification is designed to allow for the alignment being done with the car with no driver/passengers.
If the toe angle difference is out of specification, this can point to many things, unfortunately.
Such as one tie rod run all the way in and the other side all the way out. The steering rack not being center. The control arm rear mount points (FCAB) not straight and/or bent control arms. There's more but if..... the measurement is no good, I'd start there.
You still haven't answered my question; Is the car lowered?
If not, is the alignment shop weighting the car and measuring the ride height?
Sounds harsh but all but the very newest BMW dealer KDS machines cannot perform a correct alignment without first putting weight into the car and then measuring/correcting the ride height BEFORE any wrench is turned.
I can't emphasize this enough. Can a wheel alignment be done by just pulling the car onto the rack, setting the tire pressure and making adjustments, why yes. It's not correct, BMW has an insane way of doing a wheel alignment and we adhere to it.
Take your case; If it were here in my shop, how can I properly measure setback & toe out on turns if the car is lower or higher that the specification data? I'd be working with false data.
(Tantamount to using engine measurements for a M54B25 when I'm working on a M54B30)