How did the ancient Romans view race? Could outsiders “become” Roman if they adopted certain cultural traits?

by ExarchateOfBestKorea

I am aware “race” is a very contentious term - take it to be nationhood, or culture, or whatever - but I am only very dimly aware as to the differences between what seems to be the modern Western conception of race on the basis of the division of skin colors, and say, that of the Roman one, which, correct me if I am wrong, seems to have held culture and language in higher regard, such that anyone could become Roman, if they adopt enough “civilized” habits (From the Romans’ point of view)

Am I correct or wrong in my assessment? Please educate me.

mleibowitz97