As requested in the aforementioned conversation on Discord I took a look through all the bottoms with skin patterns and your theory of it being related to using the tights under skirts model instead of the normal tights one would appear to be correct as it's every pattern that uses that model that appears with the visible seam.
These are, for reference:
Bikini 2
Bikini 3
Angelic
Angelic Plus
Assassin
Athletic Shorts
Baroque
Blast
Disco
Hacker
Heart
Hearts Plus
Holes
Shorts 1
Shorts 1 + Tights
Shorts 2
Shorts 2 + Tights
Shorts 3
Shorts 3 + Tights
Straps 2
Note that these same patterns don't display the same seam when applied over tights (where they all use the normal tights model rather than being different) but only when used as bottoms with skin. The actual texture used for the pattern is the same file either way (I tested this myself by dropping a modified file over one of them and seeing if it showed up in both places which it did.) Thus I can only assume there's some workaround applied on the original legacy versions to make them appear correct on the tights under skirt model, though whether locating and redoing that would be less work than actually fixing it properly is as debatable as anything involving this game's code.
Interestingly, you speculated at first on Discord that it could be the white levels in the relevent textures being off. That doesn't appear to be the actual problem but I extracted a couple of them from the Rebirth piggs myself to see and they actually are slightly off, they have a faint greenish tint to the white parts that doesn't seem to actually cause any problems but it's there. Note that's not unique to the ones experiencing the bug with the visible seam, it appears to be all of them including the few chest textures I looked at.
New texture on the right, legacy on the left. Not sure if that's a problem worth the effort to fix but still.