Some time has passed without an answer to this question. I don't have a real answer, but will submit what I think may be the case.
First of all, no, I don't think Euripides wrote that, but it might be vaguely based on something that Euripides did write.
When I did a Google search on the passage, I found it repeated, word for word, in several books (as you say "on self-help and spiritualism"). I think the key may be in this particular citation which cites a source: "quoted in The Goddess Companion by Pat Moynihan". Doing a Google search on "The Goddess Companion" yields a book by "Patricia Monaghan", so I'm guessing the source of all these citations is in the latter work. (Unfortunately, I can't look up the citation in the latter book without buying the book, which I have no desire to do.)
So, what I think the citation might be ultimately based on is the following passage from Helen:
ὧν οὐ θέμις <σ᾽> οὔθ᾽ ὁσία
᾽πύρωσας ἐν <θεῶν> θαλάμοις,
 μῆνιν δ᾽ ἔσχες μεγάλας
ματρός, ὦ παῖ, θυσίας
οὐ σεβίζουσα θεᾶς.
μέγα τοι δύναται νεβρῶν
 κισσοῦ τε στεφθεῖσα χλόα
νάρθηκας εἰς ἱερούς,
ῥόμβου θ᾽ εἱλισσομένα
κύκλιος ἔνοσις αἰθερία,
βακχεύουσά τ᾽ ἔθειρα Βρομί-
 ῳ καὶ παννυχίδες θεᾶς.
† εὖ δέ νιν ἄμασιν
ὑπέρβαλε σελάνα †
μορφᾷ μόνον ηὔχεις.
The English translations available on-line seem to be variants of an older translation by
E. P. Coleridge. Here's one version:
Thou hast wedded as thou never shouldst have done in defiance of all right, and thou hast incurred, my daughter, the wrath of the great mother by disregarding her sacrifices. Oh! mighty is the virtue in dress of dappled fawn-skin, in ivy green that twineth round a sacred thyrsus, in whirling tambourines struck as they revolve in air in tresses wildly streaming for the revelry of Bromius, and likewise in the sleepless vigils of the goddess, when the moon looks down and sheds her radiance o'er the scene. Thou wert confident in thy charms alone.
It's pretty clear that the passage from Helen does not match the spirit of the passage quoted in various books, but it won't be the first time that Classical quotations have gotten somewhat mangled. Anyway, that's my best guess at the origin.