You stated that it is forbidden for women to wear the red strings (the ones which are supposedly tied around kever rachel) on shabbat. Why? Why is it not counted as jewellery or a bracelet?
Maybe since as apposed to a bracelet it’s not an adornment per se and not used to be worn as a piece of clothing, it doesn’t count as a Tachshit, and therefore is considered as carrying on Shabbat when there is no Eruv. (See Shmirat Shabbat Kehilchata p. 207, 212)