You are correct, it is a bug in SSMS. I’m using SQL Server Management Studio 2008 R2 and when I try to create a View using the built-in designer, I get the same error message as you:
SQL Execution Error
Error Source: .Net SqlClient Data Provider
Error Message: Cannot call methods on date.
As @Aaron Bertrand mentioned, to solve the issue, select ‘New Query’ and create the View in the Query window. For your code, it would be:
CREATE VIEW myView AS
SELECT ID, ScheduleID, ShiftDate, CAST(ShiftDate AS DATE) AS ProductionDate
FROM dbo.ScheduleResults