So I was going to do a long post about this issue, but seeing as I found the solution I thought it might be beneficial to just post the solution.
So if you have a National ID or Citizen Card and your ID does not have a start/issue date, you won’t be able to check-in through WizzAir website, the start/issue date is a requirement and is not optional. So as an example, if you happen to have a Portuguese “Cartão do Cidadão” Citizen Card, it does not have a issue date only an expiry date, you will be prevented from performing check-in on their website as the Issue Date entry will drop-down a calendar for you to choose a date and won’t let you save the details until that has been entered.
The solution to this is simple if you happen to have a smartphone, just go through the check-in via the mobile app and you will find that issue date is not a field on the required Passenger Details.
There you go a simple solution, now if you happen to not have a smartphone you can always ring WizzAir customer service and try and explain this to their CS representative who will tell you “there is nothing they can do” so they will required you to do Check-in at the Airport.
This is a case where they probably had 2 teams working separately but never bothered to check their business requirements or test their products workflow thoroughly.