Same problem as above - calendar doesn't drop down, keying in a date in the text box works just fine.
Republishing the workbook didn't fix the problem.
I am also experiencing the same issue. Upgraded the Tableau server to 2018.1 and the Calendar selector is no longer functional in the Web reports. The date selector still functions in Desktop and Desktop preview.
The selector was functional this morning prior to the upgrade.
Has anyone try it in server 2018.1.1?
Just to close the loop on this one, and for the benefit of anyone else with the same problem, Tableau seem to acknowledge there is an issue with Tableau Server v2018.1, as they have issued the following kb article