Usually, the air cleaner stud is a normal "fit" in the carb air horn. Not "nailed down", but loose enough you can remove it with your fingers. Usually, enough "tight" that you can remove the air cleaner wingnut and the stud stays put, though. In some cases, enough "loose: that you can wiggle it when it's fully screwed-in. Yours sounds like it might be a bit toward the loose side of normal, though. As long as you can snug-down the wingnut, no problems.
Some people have used a long-shank bolt (and a flat washer under it) in place of that stud, so that a socket or strong fingers can be used to remove it. "Low profile" that way, if needed.
Enjoy!
CBODY67