According to our girsa in the gemara on is obligated to remove shatnez from themselves even if it will cause them public embarrassment. The Rambam had a girsa that when one finds shatnez on their friends garment they are obligated to rip it off them even in the street. From the Rosh who has our girsa, it seems that one would only need to do this to themselves but not to someone else. The Rosh actually goes lishitaso (Nida, Kilei begadim 6) where he writes that if one sees their friend wearing shatnzes and the friend is unaware, don't tell him until he reaches a place that is possible to remove the garment without suffering embarrassment.
The Rambam and Rosh seem to argue whether the שוגג, accidental violation would allow someone else to not tell him immediately to protect his kavod habriyos. The Nodeh B'Yehuda (O.C. 35) explains based on a chakira whether on why we would push off an issur בשב ואל תעשה for the sake of kavod habriyos as we find in the end of the gemara. If שב ואל תעשה is just a lower level aveira, but when the aveira is being violated בקום ועשה such as when someone is wearing kelayim, there is a requirement on the one who knows to tell him. Or if the point of שב ואל תעשה is that one has the right to be passive, so too the one who knows has the right to be passive for כבוד הבריות and not inform the one wearing the shatnez. The Rambam would hold that since the prohibition is being violated by the active wearing of shatnez, it is not considered passive and you must tell him. However, the Rosh holds that since the one who knows is just being passive by not telling, he has the right to do so for the sake of kavod habriyos even though the prohibition is being violated actively. See Sha'agas Aryeh (58) who makes this issue dependent on two answers of Tosafos in Shavuos 30b.
The gemara asks from the statement of גדול כבוד הבריות שדוחה את ל"ת שבתורה, that one can violate a prohibition to protect kavod habriyos. The gemara responds that they can only violate לא תסור. and then explains that all Rabbonon's are supported by לא תסור, but where it interferes with kavod habriyos, they were lenient.
There is a well known argument between the Rambam and Ramban whether all Rabbinic prohibitions are automatically upgraded to be like a d'oraysa based on לא תסור. The Rambam holds it is like the violation of a d'oraysa, whereas the Ramban says that it is only the violation of a d'rabonon. The Ramban would learn the gemara here to say that לא תסור is not more than an אסמכת to find so hint to the concept of listening to the Rabbonon from within the Torah, but in truth the pasuk is not a real source for anything. However, the Rashi seems to imply like the Rambam. Really every derabonon is supported by לא תסור, just that the Rabbonon had the foresight to lower the bar and be "mochel" on their restrictions in pressing circumstances such as kavod habriyos. Therefore. although לא תסור is a source to support d'rabonon violations, and kavod habriyos is not powerful enough to push it off, the Rabbonon never implemented their decrees in a situation where there would be a conflict with kavod habriyos. According to the Ramban we don't need to say that רבנן אחלוה ליקרייהו לעבור על דבריהם היכא דאיכא כבוד הבריות, which essentially means that the issur d'rabonon doesn't apply to such a situations, rather simply that kavod habriyos is more powerful and trumps the issur d'rabonon.