The idea of an "oblate" as something other than a child donated to a monastery, is rather a post-Schism concept, sort of a third order idea, which however has been found useful for laypeople as a way to enter into a supportive relationship with a monastery, and this idea of being an "oblate" is something which has been accepted and is treated as a serious calling or way of life for a layman, by our Orthodox Benedictine monasteries.
Christminster and Our Lady of Mt. Royal have oblates, and there are some Antiochian oblates who, in a pan-Orthodox spirit, receive instructions and guidance from a ROCOR abbot.
I was aware that Christminster had oblates, but thanks for letting me know.
As for the rest, there was indeed a resurgence of interest in being a Benedictine Oblate more recently in the life of the Catholic Church. At what point oblates "officially" started being recognized as adults seems to be up for some debate, but the practice of a relationship with and participation in the life of a particular monastery has been around for a very long time.