I just tested this with a dummy workflow to make sure I wasn't telling you the wrong thing... :)

If the date field is not required I was able to bring this in by writing a blank field value, or even assigning a blank token. Either way worked, the date went away using the default "general" template in my test 9.2 system. 

If the date field is required you get a similar error message that says "one or more required fields were omitted" when I made the date field required.

However what I suspect that may be happening with your error is that you are pulling data from something else such as a database or PDF. In that case the data being pulled is most likely 'NULL' which is not the same as 'nothing'. I know I've run into this before when trying to retrieve data off of another source, and what I end up having to do is use a conditional to test if the date is a valid date, then use an assign with that token if it is and a assign with no token if it is not.