Sorry to go on at such length about this, but since we're dissecting why Wiccans insist they have a right to participate in cultural appropriation, there's a significant amount of material to cover.
The problem is, even Wiccans come out of the Western tradition which is based on Christianity, in which God is for everyone. So this concept gets applied to Pagan traditions as well... to deny someone access to a God (or Goddess, or spirit, or fairy, or totem animal or what have you) is considered horrible and wrong.
In Western thought, the person is being denied salvation or spiritual enlightenment.
I guess Christianity (or rebellious rejection of Christianity) could have something to do with it, but it's also plain old white privilege.
Not all traditions that can be classified as "Western", Pagan or even Neopagan function that way. Ethnic reconstructionists, revivalists and traditionals do not mix and match, do not steal other people's traditions or spirits, and I don't know any who conceptualize their way of life as seeking "salvation" or "enlightenment". Wicca is only one of the vastly different traditions that outsiders lump together as "Pagan".
Though mainstream attitudes can certainly influence everyone who comes into any contact with the mainstream (say, via TV and Hollywood movies), many of us (and most of the members of this board) were not raised Christian.
If we're going to blame attitudes that have bled over from Christianity for the problems in Wicca, the Wiccans (and members of Neopagan trads derived from Wicca) should understand that their cultural appropriation - thinking they can redefine spirits and lead ceremonies for their confused, outsider fantasies of spirits from cultures they don't belong to - is more like reading a webpage about Baptists then claiming they can offer people Catholic communion; and as they lead their fake communions and confessions, ignoring the fact their fake ceremony is being picketed by Catholics and condemned by the Bishops.
Just one thing though, "The all Gods are one God" quote is not core to Wicca, it's from Dion Fortune's novel "The Sea Priestess". Dion Fortune was into esoteric stuff, yes, but she was Christian not Wiccan. None of the trad Wiccans I know would agree with her quote.
Yes, the quote is from Dion Fortune, a ceremonial magician who laid the groundwork for a lot of what the English and English-descended occultists do (as did Aleister Crowley and the Golden Dawn). Her branch of Hermetic Ceremonial Magic has had a huge influence on BritTrad Wicca. While neither Gardner nor Valiente wrote that bit, many Wiccan groups have incorporated it into their theology, as it encompasses the attitudes in the original Gardnerian materials: ritual scripts where deities and spirits from vastly different cultures are listed, lumped together, "invoked", and all considered "aspects" of one, universal "Great Goddess". This idea of a world-wide religion that was essentially the same in all ancient cultures was not a view held by the cultures Gardner vultured from, but that didn't stop him and his descendants from swiping, twisting and misrepresenting all those different cultures.
Gardner was a product of British Colonialism, and believed his people had the right to colonize and conquer the world. The religion he created reflects that.
In terms of source material for Wicca, I would say it's a tossup between Gerald Gardner's fantasies about Plains NDNs and stuff stolen verbatim (once translated into English) from Hinduism. The reason for the terms and "tools" and theology lifted from Hinduism and Indigenous Asian tribes? Gardner lived and worked in the parts of Sri Lanka and Malaya that were under English colonial rule at that time, first as a plantation manager then as a government employee. His father owned one of the plantations he managed. Gardner was directly responsible for enacting and enforcing colonialist policies.
It may be different where you live, but I have met Gardnerians and Alexandrians who have incorporated the Dion Fortune quote (and other writings of hers, along with things by Robert Graves and other writers) into their rituals and "Book of Shadows". Some BritTrad Wiccans stay strictly by the book they got from Gardner and Doreen Valiente, but as the initial version of even the 3rd degree materials was very sparse, most lineages have added to theirs considerably. During the eighties I was friends with, and was a guest at some rituals of, friends who were BritTrad, including members of the first Alexandrian and Gardnerian groups in this country; most of the BritTrad people in the US trace their lineage to them. Note that during this time the heads of those lineages knew about the ahistoricity of Wicca; the head of the Alexandrian line in particular had come to the same conclusions as Aidan Kelly (author of Crafting the Art of Magic) and other researchers. Kelly's manuscript had also been in private circulation for many years at that point. After Kelly published, a number of Wiccans changed their backstories; some of them even changed the names of their traditions and created new, earlier "initiators" who they claimed were not Wiccan at all. I guess they think people have short memories.
If I sound argumentative or ranty I apologize. I'm just sick of seeing privileged white people use bad theology and inaccurate history as an excuse for racist behaviour.
Oh, and Deb, you're right - even though the exact quote is from Fortune, the idea that there is one, universal Goddess and God pair who encompass all the spirits and deities of every culture in the world is also held by Jungians and Goddess spirituality groups who have no direct connection to Dion Fortune or her tradition of Ceremonial Magic.