Are stages of enlightenment obsolete and old fashioned?
No, they don’t - the stages are real. They are ultimately illusory because they are all layers of the dream, but they are real in a sense that an individual on the path, should they not stop and follow it to completion, necessarily goes through stages which an enlightened individual can easily identify in all but very distorted ancient texts, and in writings of similarly enlightened individuals, also, no matter what language they use.
They aren’t always linear, and there could be some back and forth, but sooner or later, when all settles down (usually, after many years), they still can be identified in others’ writings.
The vast majority of people who reject stages are themselves in a stage. Usually the first one, otherwise they wouldn’t reject them altogether. So they are awake, or self-realized, but not enlightened yet, there’s more for them. “There’s always more!” - they would say.
I usually say that there are no levels of enlightenment, but there are levels of dreaming. Ramana said once that there are no levels of realization, but there are levels of experience. These statements refer to the same phenomenon.