The dictionary says it's a noun, but I'm not even sure how to use it as a noun in English. Could someone please give me examples? Is there a way to put it into verb form? For example, saying "I'm not getting involved in their argument".
Or is my only option 巻き込む (e.g. 彼らの議論に巻き込まれたくない - I don't want to get involved in their argument)
巻き添えにする means the object suffers, whereas 巻き込む doesn't always mean the object is damaged from it. Also, 巻き添え is a noun, so you need to pay attention to the choice of the particles.
e.g.
彼は彼らの論争の巻き添えにされた。
彼は彼らの論争に巻き込まれた。