The gemara says a rule that whatever would be considered a chatzitza to prevent water from penetrating and therefore have to be removed before immersing in a mikva, would be forbidden to wear on shabbos out of fear that one may remove it and carry it. The gemara offers an איכא דאמרי which says that something that is dirty, although it allows water to penetrate is forbidden - כיון דטניפא, מקפד קפדא עלייהו - since it is dirty a person tends to be makpid and not want it there. The point of the gemara is to say that one may not wear such an item on shabbos in the public domain, but it isn't clear whether the gemara is insisting on the removal even for immersion in a mikvah.
Rashi explains that since water can easily penetrate there is no issue of chatzitza and one may immerse with this item. However, since it is dirty and by bathing with it on, the residue mud will get on a persons skin, they will definitely remove it prior to immersion and therefore forbidden to wear on shabbos for fear that they may carry it. However, Rashi citing his Rebbeim - רבותיו של רש"י, explain that even though water penetrates, one may not immerse in a mikva while they are wearing something that they are makpid about and don't want to be there. The רבותיו של רש"י create a new concept that even when something doesn't block the penetration of water, it can still be considered a chatzitza and must be removed for tevila. Although they write that this is when one is both makpid on it AND it covers the majority of one's body or hair, it would seem that just as by a real chatzitza the Rabbonon make a gezeira for anything that one is either makpid about OR covers the majority of their body, the rules here would be the same [this is the assumption of the pischei teshuva y.d. 198:4; whereas the Sidrei Tahara writes that the gezeira would only be extended to a case where one is makpid, even on part of their body, but not to a case of רובו שאינו מקפיד. Rav Moshe (dibros) even suggests the possibility that on this type of chatiztza there wouldn't be any gezeira at all and it would only be a problem if it were both רובו and מקפיד].
The Sha'ar HaTziyun 303:4 points out that the Rama seems to contradict himself. The Rama in Y.D. 198:4 writes like the רבותיו של רש"י that something can qualify as a chatzitza even if it doesn't prevent water from penetrating. Yet, in O.C. 303:1 the Rama explains this gemara like Rashi - something that is dirty even though it doesn't block water and doesn't need to be removed for tevilla would still be forbidden to wear on shabbos since practically speaking one will remove it before immersing to prevent the mud from getting on their skin. Why does the Rama in Y.D. assume like רבותיו של רש"י, yet in O.C. assumes like Rashi? If we were to say that the Rama is machmir in Y.D. like רבותיו של רש"י, but in Hilchos shabbos is machmir like Rashi, we could suggest that the Rama paskens like both l'chumra. However, it is difficult to see how the approach of Rashi could be a chumra and more restrictive than the approach of his rabbeim.
In general when we define the concept of מקפיד in the context of chatzitza for immersion we refer to anything a person wants removed during normal activity, either for their own sake or for the sake of the item. However, when Rashi describes the concept of makpid that will lead one to remove the item prior to immersion he is speaking about something that has some dry mud on it which one will remove before immersing to prevent themselves from getting dirty. It is possible that this type of makpid would not qualify as a chatzitza for mikvah. The definition of chatzitza for mikvah is something that in general one doesn't want to be there (either because it bothers them or they are afraid of it getting ruined) and therefore isn't batul to their hair or skin, but here she does want these woven threads to be there and isn't technically makpid about them even when she immerses, just that since it will leave some residue afterward she will remove it to prevent herself from getting dirty. It is not the woven material that she is makpid about, rather the mud that will get on her afterward, therefore the woven threads wouldn't be considered makpid and be batul to their hair (obviously, it is possible to argue on this assumption and consider even something that one will remove to prevent themselves from getting dirty when it gets wet to be considered makpid). According to this approach, something that is dirty on the inside and will leave behind a residue of mud on her skin, but isn't dirty on the outside, would qualify as makpid according to Rashi but not according to רבותיו של רש"י. Therefore, it is possible that although the Rama is machmir for רבותיו של רש"י in hilchos chatzitza, he still is machmir for Rashi's definition of makpid and cites Rashi's approach in hilchos shabbos to forbid wearing on shabbos even something that will leave behind some residue and therefore one will remove it before immersing even though in the halachos of chatzitza it wouldn't qualify as makpid so that they wouldn't be required to remove it (even according to רבותיו של רש"י who require things to be removed when water penetrates, that is only if it qualifies as makpid).