Bins are not causing the yarn cloth problem, but they cause a lot of cancellations because access to a bin locks out all other access to the same bin during the access, and since jobs select the specific item(s) to work with, blockage of the access of an item at the time the game tries to collect it causes the job to be cancelled. Disabling notification and using the manager hides the symptoms to some extent: things just take longer than they should. Bins are partially broken and act as a newbie trap.
What I did immediately before discovering the game was modded (and hence that no DF assumptions can be relied upon) was to remove the stockpile the cloth was in, paint a cloth stockpile in the room the clothier workshop was in (i.e. around it), painting a dump zone over that in the top left corner of the room, and mass dump everything in the cloth stockpile. Cloth of various kinds were dumped, but unforbidding it allowed plant cloth to be used, but not yarn cloth, despite it now being in the same time, ordered by a re-build workshop.
A fundamental question for anyone who would try to fault find it for you is whether this suddenly stopped working (as the original post seems to indicate), or whether it never worked. If it was the former, I'd guess you've modified some mod setting to make yarn off limits, somehow. If it's the latter, the mod is likely broken.