Years ago, I wove a blue and white “plaid” twill towel, with 1/2″ or so of plain weave on each end, and hemstitched on the loom (above). I didn’t recall any issue between the plain weave hems and the twill body of the towel. Both warp and weft were Swedish cottolin.

Since I still had the sample (above) from the very beginning of the warp, and both samples had ripples, both were tossed into the washer (regular cycle, warm water) and drier (normal cycle), removing them while still slightly damp. When they came out, the ripples were more pronounced. When pressed with an iron, the ripples pressed out. Selvedges were still a bit of an issue where plain weave and twill changed. Edges were rotary cut, and photos taken.
Tomorrow morning, I will begin again, using a single strand of the linen/cotton slub for both hem and twill, which should alleviate some of the problem. I expect if I weave 1/2″ or so hem and hemstitch on the loom, there would be little or no ripple effect. We’ll see, on this towel, or the next.