Not possible in PDF forms. You would need to use a web form, I think.
I have been trying to use these instructions in Adobe Acrobat Pro DC using the "Prepare Form" tool instead of the "Select Object" tool specified in the instructions. When I switch back to "Fill & Sign" it does not let me select a date. The calendar field does not fill in at all. I have all the values selected from the original form and they are not overlapping with other fields.
It's hard to believe that such an advanced program does not have a calendar feature.