I would imagine that the Air Acolytes stayed right where they were and continued to do what they'd been doing for seventy years, which is to take care of the various Air Temples. Remember that as of Book 4, there are still very few new airbenders.
And to me, there is absolutely no reason for the Air Acolytes to go anywhere simply because they're not airbenders and there are other airbenders besides Tenzin and his immediate family.
Yeah. I think the Air Acolytes are more of a cult or a religion, then a bunch of slaves who do anything Tenzin says. The Air Acolytes wish to live that way of life...or at least the way that Aang taught them. It is probably voluntary, like any religion. Aang was probably a great master and teacher, so many thousands of people might follow his beliefs. Maybe he wrote some books on Bending, or Air Nomad Culture, taught benders about other bending styles, or even wrote self-help books and training manuals for non-benders. Some of his most loyal followers probably never met him. I think a guy like Aang wouldn't reject anyone from self-improvement.
So there might be Air Acolytes that don't even live in temples anyway who merely follow their master's books and teachings. There might be Air Acolyte clubs where they discuss these things in detail and pass out pamphlets and free books. It is probably only the most devoted of Aang's followers who were allowed to live a monastic life, because it is extreme lifestyle. Or later a sort of Chivalrous Adventurous life on a blimp, that is even more extreme. There are probably many Air Acolytes ranging from "people who own all of his books" to "people who go to Avatar club twice a week" to "People willing to jump off a train and beat up Kuvira." Even though in the old nation Air Benders might have been in charge of everything, I can't imagine kind, simple, egalitarian Aang forcing every one of his students to worship Air benders for no other reason than their abilities. IT is interesting that Aang has both a political and religious legacy in this world.
They're probably still there; there aren't really enough airbenders to do all the work they used to do, so they'd still be needed. Plus, i doubt Tenzin would just kick them to the curb after working for him for so long.
Since the Water Tribes started as just one tribe in the North Pole, and several of its people traveled to the South Pole to engineer a new tribe where their traditions developed different from the Northern Water Tribe's.
Evan Gran-Gran left the North Pole because she didn't want to marry Pakku when she didn't love him (at the time).
The Air Acolytes still, and will always exist. They are just as much a part of the Air Nation as it's benders, If anything The New Air Nation new is composed of both benders and non-benders. I even believe that there are people who bend other elements as children of acolytes aloowing the new air nation to exterience a culturally diverse upbringing which makes their life even better.