I use the option “disable event-search bar” in event calendars settings to stop the search bar from being displayed. This hides some parts of the bar but the date-field is still visible. Example: https://www.nordicfit.com/termine/
What can I do to hide this field like the others?
I also realize that the behavior of this field is different from your demo on http://wpshindig.com/events/
On your demo it displays clickable tiles for every month which would make more sense for us than letting users typing individual dates in this field.