We are to take off the prayer rope before a service. Prayer ropes are private prayer and services held at church are communal. When a bishop is greeted at the entrance of the church before liturgy he in fact takes off his prayer rope for this specific reason.
I don't know if the women are still with us but I know up until a few years ago I know a cathedral where a few ladies would say the rosary before liturgy. To quote their late bishop, "leave the women who say the rosary alone, they're not hurting anyone, they learnt it in Catholic school 70 years ago". In fact it was just a tiny few that I saw doing so.
Also I do have a humeral veil in my possession from an OCA parish (priest had vestments he wanted properly disposed of, I got the humeral veil and kept it as a historical piece). At one time the parishes in the area and even Pittsburgh had a form of benediction of the blessed sacrament, Saturdays I believe in Lent. Didn't matter if it was OCA, ACROD, UOC-USA and I don't know about ROCOR/MP. Even my parish still has a humeral veil in the vestment closet left their for posterity.
Last time I saw benediction in an eastern setting was a number of years ago when we were Greek Catholic at the Uniontown Pilgrimage. I hear they even stopped.
Issue is to discern what is part of the recension of a group of believers and what is a latinization. Not everything is a latinization. clearly rosary is.
And no you don't wear a rosary like jewelry. Did not Christ say to keep your private prayer private?