Is there an issue with wearing a cap and gown? I am thinking perhaps this could be an issue of chukas goyim (dressing like the other nations). Further, is there an issue if the college for which you are wearing it is a religious (not Jewish) college?
According to Horav Yosef Yeshaya Braun, see Halacha2go, a graduation gown or cap is considered as something you wear for a specific purpose and therefore not considered as chukos hagoyim:
Medical apparel, graduation gowns or other types of uniforms are worn for a specific purpose, and are therefore not considered chukos hagoyim. On the other hand, ripped jeans or other fashions that essentially have neither taam nor toeles can be categorized as chukos hagoyim. Flashy fads that push the limits of modesty and involve derech pritzus, such as certain popular hairstyles, are also a halachic issue. With regard to all modes of dress, the rules of reasonable and useful fashion apply.
Ha-Rav Moshe Feinstein also has a responsum on this issue in "Igrot Moshe" (Yoreh Deah 1:81). He was asked if there is a requirement to wear the clothing which Jews wore in Poland, since in America both Jews and non-like dress alike. Ha-Rav Moshe answered that it is permissible to wear the clothing like the non-Jews since there is no unique type of Jewish clothing, and even G-d–fearing Jews wear the clothing like the non-Jews.
See also: Jeans as Hukot HaGoyim
Rav Moshe Feinstein (quoted in Mesoras Moshe vol. 2 pg. 196) says it is forbidden to wear a cap and gown because the custom of wearing them to a graduation started with priests in their colleges. He says it is abizrayhu of avodah zara and was surprised that Yeshiva University graduates wear a cap and gown to graduation.