Rav Aviner was asked if one is allowed to wear a nose ring. Assuming it is problematic, why is it any different than an earring? Some religious women wear them, though not Haredi women and not Dati women with yirat shamayim, and Eliezer gave Rivka a nose ring... so what's the deal?

Rav Aviner responded nose rings are prohibited due to the rule of "chukas hagoyim" - imitation of non-jewish practices. He explains that not everything goyim do turns that thing into chukas hagoyim. There are rules. One rule of chukas hagoyim is supplied by the Maharik who says that something that is immodest that is attracting, such as red clothing, is chukas hagoyim. If it is immodest, it is prohibited anyway, but if it is something the goyim do, then it is also  the additional prohibition of chukas hagoyim. Rivka wearing a nose ring is no proof of anything because at the time it was commonly worn.

Rav Moshe Feinstein quotes the Maharik in regards to prohibiting the wearing of clothes in a haughty way - meaning, clothes that make an impression, that attract, that the wearer wants people to see and notice. As the Orchos Tzaddikim says that wearing attracting clothing is a form of "gaiva" - haughtiness.

Rav Chaim of Tzanz that someone wearing both modest and immodest clothing is transgressing a negative prohibition and deserves lashes, even if the intention is not to appear like the non-Jews, even if one can tell from the clothing that she is Jewish and only one item is similar to that of the non-Jews, it points to a lack of modesty.

The rule is, Rav Aviner says, a woman does not need to try to look beautiful in public. Beauty is for her husband, and her desires should be to serve God.
source: Srugim

The concluding rule does not seem to fit with the rest of his explanation. In his explanation he talks about what qualifies as chukas hagoyim, and in his concluding rule he makes a comment on women looking pretty in public. One has nothing to do with the other. A woman can look pretty or attractive in public without transgressing chukas hagoyim, and without transgressing rules of modesty. A woman can look ugly (is that the opposite of pretty?) and still transgress chukas hagoyim.

One might say that nose rings have become common enough, among Jewish women, that it is more similar to Rivka's days of it being common and therefore acceptable, than a problem of chukas hagoyim. Maybe the first women to wear them were dabbling in something problematic, but once it becomes common among Jewish women it would no longer be considered chukas hagoyim.