Fillable form date dropdown without custom text

By "dropdown" do you mean the calendar/date picker that's displayed when you format a field as a date?  The field should only accept a date in the format programmed to that field.  Are you trying to force someone to use the calendar and prevent them from manual data entry?  I developed a PAID tool that puts a button next to a text field that triggers a popup calendar/date picker.  If you set the text field to read only, the user will have to use the calendar to enter the date:

https://www.pdfautomationstation.com/products/item7.cfm

You can't prevent someone from manually entering a value into a Date text field, if that's what you mean, but if you set it with a specific date pattern it should only accept that pattern, even if entered manually.

What selections do are you trying to put in the dropdown?  The current date?  Enter the follow script as a mouse down action in the dropdown:

event.target.setItems(["",util.printd("mm/dd/yyyy", new Date())]);