Modern Paganisms are reconstructions and recreations of old religious traditions; there is no continuity of culture or belief.
This question could be asked of any religion or spirituality that has a long history, including Christianity, Islam and Hinduism. No culture is static, no beliefs are unchanging. Many religions have developed over long periods, and have been transplanted into different lands, yet fully retain their spiritual essence. All religions must adapt in the face of new knowledge and understanding. The Christianity that is practised in the British Isles today is unrecognisable from that which developed originally in Palestine in the first centuries CE, or from that which arrived in Britain in the sixth century CE – yet its spiritual intention is the same, and the continuity is acknowledged.
So it is with Paganism. With the coming of Christianity to Britain, indigenous religions were suppressed, their beliefs remembered and perpetuated as superstition and folklore, their gods becoming demons and evil spirits. Over the past three centuries or so, and particularly during the past 50 years, people have been re-discovering these practices, seeking a spirituality or religion that reconciles a nature-based philosophy with the pre-Christian ancestral heritage of the British Isles, creating the modern Paganisms. The continuity is not necessarily in the practice, but in the spiritual intent of those who are drawn to it – as is true of other religions.
Having said that, within many strands of Paganism, there are gods revered now that were honoured two thousands years ago and more, prayers and invocations used that were spoken by our preChristian ancestors, perspectives, ontologies and beliefs carrying through into the modern day.