I am in the same position, my Halifax Debit Card worked fine, but my Ulster Bank Debit card does not.
I got the same answer; it needs to be a Credit Card so that we are sure the person is over 18.
However that argument is just wrong, because it is possible to get an additional card holder that is under 18 with MBNA for example.
I liked to play online lotto rather than going to the shop and found that using my debit card is my preferred choice rather than my credit card. If AnPost codes the transaction as gambling one might get problems with the card provider as some regard gambling with different APR and also bad for account reviews.
They could just offer that you proof your age by uploading a passport copy and then enabling Debit cards. But I assume that would create too much cost.