IMO tire +- tire diameters that will generate warning light(s) or error codes from side to side or front to rear are confusing and inconclusive.
One reason is that I see no indication that posts are about a particular transfer case or all E53 transfer cases or transfer cases in general. As many know, there are two E53 transfer cases. One used from 2000-2003 and one used with xDrive from 2004-2006. The earlier transfer case was mechanical with a constant percentage front and rear. The xDrive transfer case is infinity variable and operates in a very different way.
Another is that for most of the posts there is a counter-post. Since I don't know the credibility of one verses the other, I don't have a clue if either of the posts are correct.
In addition, I can't find a BMW technical paper on how each operate, the impact of tire size on the transfer case or on the intended operation. Nor have I read a BMW generated percentage of how much variance is too much. I would guess there is one and would like to read it. Anybody know a source?
I can find where BMW states that different makes of tires may cause DSC to overreact and another where BMW states tire size is critical to proper operation and also one that states if the DSC is not operating properly it will generate error codes--all without any details. The only thing I think I know is that some amount of tire diameter or tire brand differences will compromise the effectiveness of the DSC system.
From personal experience I have never had a DSC problem related to tire size. At 110,000 miles I still have the original transfer case and never had a problem. I have replaced a single tire due to a blowout where the tread depth was then quite different than the other side. I have replaced tires on one end or the other many times as I go through rears twice as often as front tires. I have had different brands on the front and rear. I have had two different brands front and rear where the tires on the other end were down to half the tread depth. I have had to drive over several miles on deflated tire. I have noticed a low tire and had to drive 20+ miles before I could correct the 8 pounds it was low.
Thus far my conclusion has to be that some degree of tire differences front to rear or side to side may cause error codes or cause the DSC to over react but nothing else that is significant enough to mention.
that OP should, in some manner, get all tire diameters to as near to the same height as possible and see if the problem goes away because that would eliminate the question if variation in diameter is the problem. Might be able to safely achieve that goal using inflation.