I'm reading a book written in the 1800s where a people called themselves Anti-Lehi-Nephi. This people called themselves this to be different then their allies the "Nephites". Did "anti" mean the same thing back in the 1800s? These people were not against or opposed to the other group of people. They were very much allies.
The Book of Mormon Archaeological Forum has posted an article by Stephen L. Carr that is devoted to precisely the question you ask, "The Name ‘Anti’ in the Book of Mormon." According to Carr:
The usage of the names, Anti-Nephi-Lehi and Anti-Nephi-Lehies has provoked considerable discussion among L[atter]D[ay]S[aints] Book of Mormon scholars and lay members alike. Anti-Nephi-Lehi was the name given to the son of the chief Lamanite king in the greater land of Nephi after his conversion to the true gospel. His previous name is unknown in the Book of Mormon. (The father king then died and this newly renamed son became king.) This was done, apparently, in honor of the conversion of many of the subjects of both the son and the father to the gospel as taught by Ammon and his brother Nephite missionaries and a few other companions. Subsequently, all the converts of the father (whose name is also unknown) and, presumably, the son, as well as the converts of Ammon and king Lamoni, who was king (and brother to Anti-Nephi-Lehi) over the local land of Ishmael of the greater land of Nephi, became known as the Anti-Nephi-Lehies.
So Anti- in this context may not signify opposition to something; the only indisputable thing about it is that it was part of the future Lamanite king's name. As for the king's subjects, they were (again according to Carr) called Anti-Nephi-Lehies. For further inquiry into how various Book of Mormon scholars and commenters interpret the "Anti-" part of the king' name, I refer you to Carr's article.