If someone else comes across this post with the same problem, which I had, then I solved it this way.
In my page load, I set the value of the textbox that was readonly to a specific value. In my case the readonly text box was a date, so I set it to today's date. Then the jQuery date selector worked it's magic and the value was saved properly, and the required field validator can be removed...well you have a valid date in place now, and it's really the user's fault if they don't change the date to something more appropriate for it's purpose, and the user can't empty the field.
Anyways, set a default value and it's all good to go, but you will still need to ask for the correct value via Request.Form[txtDateOf.UniqueID] as the standard way will always contain the default value.