This functionality is not possible in Responsive Forms unfortunately.

This is a late reply but this can absolutely be done.

Using a custom rule with some JS you can check the values of the date controls in sibling repeating section rows, and invalidate any rows with matching dates.

Here is a simple example

I’ve made a form with a Repeating Section, and a Date Control:

(Important!) I’ve named the Date Control so that I can reference it using this name later in my code:

But after my controls are on the form, I create a Validation Rule for the Date Control:

The following code can be copy / pasted:

(function(rowIndex, sourceContext) {
	var targetControl = NWF$("#" + rowIndex);
	var selectedDate = targetControl.val();

	var siblingRows = sourceContext.siblings(".nf-repeater-row:not" + "(.nf-repeater-row-hidden)");
	var siblingDates = siblingRows.map(function(index, row){
		return NWF$(row).find(" data-controlname='control_SomeDate'] .nf-associated-control").val();
	}).get();

	if (siblingDates.includes(selectedDate)) {
		return true;
	}

	return false;
}(rowIndex, sourceContext))

Saving and running the form results in the following:

Let me know if this helps