It's not officially dropped, but they haven't hosted since 2009 and venues are now set until 2021. I believe 2022 is likely to be Muirfield. So would be at least 14 years for a 2023 venue.
Most venues are used every 10 or 11 years, other than St. Andrews every 5.
I would be surprised if they announced Turnberry as a venue while Trump is president.
Talking to an employee at Turnberry this year they are of the opinion that they will not get an Open whilst Trump is president, no great shock there. They expect to be back on the Rota when he returns to civvy street. I'm sure everyone at the club is hoping he is a one term president.