… by 300 AD the Welsh were Christianized …
I’d be careful with older literature. The field of Celtic studies has undergone a lot of shifts and changes in fifty years and archaeological discoveries along with the development of historical genetic history has altered many previously-held notions.
I doubt that Wales was fully Christian by 300 CE. That Christians were present in Roman Britain before the Edict of Milian in 313 CE is not an issue, but the historical facts, texts and archaeology don’t really back up the assertion that we are dealing with a fully Christian area at that time. Constantine himself was not a Christian until the end of his life and the Edict of Milan was actually an edict of tolerance for all religions. The whole Roman Empire did not suddenly become Christian overnight and the great age of the Celtic saints wasn’t until about two to three centuries later, which means there was plenty of time for syncretism and for old beliefs to linger on – especially in rural or remote areas, whence paganus – a person of the countryside.
The Saints Julius and Aaron were said to have been martyred in 304 CE, although the date may be up to fifty years earlier – roughly contemporaneous with Albanus, or Saint Alban, who was martyred for “blaspheming the gods”. The historicity of these figures is open to debate, however, we are talking about roughly the same period. On the other hand, Saint Alban (as many other Celtic saints) was beheaded and some have suggested that they may represent a pre-Christian “head cult”, with all that entails. Either way, this would not suggest a fully Christian society and culture at the time at all. Another fact to consider was that there was a pagan revival under the emperor Julian the Apostate and a temple dedicated to Nodens, albeit a Romanised version, at Lydney in the Forest of Dean, dates from around that period in the mid-4th century CE.
In addition to this, as Greywolf has pointed out, the Romans did not really conquer or hold on to what is now Scotland, the Britons/Celts north of the wall, would in all likelihood have held on to their beliefs far longer. Indeed, Gwenddoleu ap Ceidio, a Brythonic chieftain who ruled an area around northern Cumbria and the Lowlands of Scotland and who died at the Battle of Arfderydd in 573 CE was said to have been a pagan.