I think it should be possible if you are using a field (and not a variable). Create a list box object for the field you are using in the calendar object and select Always one Selected option. Delete the list box and it might work for the calendar object.
NOTE: I have never done this before, but this technique works for Multi Box object.
Yes once 'Always One Selected' option is selected, you won't be able to clear the field. You might want to consider an alternative in that case. What exactly are you trying to do?
When you say clear, you mean that even if a field is filtered by the date selection, it should be cleared? That to me doesn't seem to be possible, because as soon as you will make a selection, fields which are out of scope will turn grey in the other field's list boxes. May be use a variable instead of date field?
