Spengler's theory of the rise and fall of cultures was highly, explicitly superstitious--very attentive to omens, symbols, astrology, etc.

for example,

The fifty-year interval of these critical points, which is seen with special distinctness in the clear historical structure of the Baroque, but is recognizable also in the sequence of the three Punic Wars, is yet another hint that the Cosmic Sowings in the form of human lives upon the surface of a minor star are not self-contained and independent, but stand in deep harmony with the unending movedness of the universe. In a small but noteworthy book ... the relation of those war-periods with weather-periods, sun-spot cycles, and certain conjunctures of the planets is established, and a great war foretold accordingly for the period 1910-10. But these and numerous similar connexions that come within the reach of our senses ... veil a secret that we have to respect and not to infringe with causal expositions or mystical brain-spectres.

Consequently, race--and the various pseudo-scientific rationalisations it encourages (climate, geography, breeding, genetics, etc.)--are drowned out by more transcendental, syncretic explanations (these are definitely not your run of the mill prejudices). That isn't to say he wasn't interested in it, or that his views, when he had them, were not pretty problematic. For starters, the decline of the west is pro-Germany, pro WWI in places--supporting, arguably, the various racialist arguments going around at the time. Secondly, the book is primarily an attack on multiculturalism (liberalism, tolerance) and a justification of nationalism, which easily slips into racism, whether it is emphasized or not. Any kind of totalizing weltanchaung is going to get into trouble somewhere of course, but Spengler's critics were less concerned by his racial stereotyping than by his blatant, aggressive superstition. He was very critical of science for example, dismissing relativity. Conversely, mathematics was central to his theory, meaning his arguments tended to based on abstract ("philosophical") concepts--being and becoming, "faustian" man--rather than trite distortions of biology.

I wouldn't however be surprised if he said something about the "rising tide of colour." But certain factors may excuse or at least contextualise the statement. He was a visionary writer, whose prose style was built on striking paradoxical aphorisms; so even on dry subjects he writes with a rhetorical extravagance that makes him sound hysterical (but not populist). He saw himself as a kind of blend of Goethe and Nietzsche; combining the organic pantheism of the former with the critical audacity of the latter. And like both, his attitude towards "action"--as opposed to art--was rather ambivalent; he is torn between admiration for the Great Men, the shaping forces of humanity, and appreciation for the many fruits of the vita contemplativa. (TDOTW is filled with a gleeful (sadomasochistic?) contempt for the pretensions of mere littérateurs, who are powerless against the Deeds of the practical men of the world). If he did say it, it's therefore not unlikely that it was expressed regretfully re: the "western canon" he loved being subsumed by races with their own ascendent traditions rather than an attack on the inferiority of those traditions themselves (he was in his own fashion a cultural relativist--as long as they stayed put). Cubism, in its debt to alien cultures, was thus judged by him as a corruption of the western cultural morphology / teleology:

The end is a sunset reflected in forms revived for a moment by pedant or by eclectic — semi-earnestness and doubtful genuineness dominate the world of the arts. We to-day are in this condition — playing a tedious game with dead forms to keep up the illusion of a living art.

Actually, because he had already--theoretically--given up "the white race" for dead, due to its degeneration from "culture" to "civilisation," it may even have been a neutral statement: that it is now their turn at the wheel. The whites had irretrievably sold out to mindless commercialism, they deserved to fall. Of course, as I said, his views are so extravagant you never really know where he is coming from; more than likely, it functions both as a warning (the white race better get their house in order or else!) and as a "disinterested" judgement about the inevitability of the great cycle (everything that goes up must come down, all that lives must die; an idea partly derived from Nietzsche's eternal return). His outrageous determinism makes it difficult to turn any of his views to practical account, or even identify them with any conventional position without losing the peculiar meaning they have within his framework (his own political ambitions never worked out for this reason) .

Ultimately, his views on race, intimately connected with his elitism, are probably very similar to Nietzsche's; they definitely have dangerous connotations when release into gen pop (and some racists did take him seriously), but are not in themselves, words on the page, especially offensive--except to humanity in general. and I'm pretty sure, tho not certain, he explicitly disavows anti-semitisim somewhere in TDOTW. At any rate, the Jews are barely mentioned at all, let alone identified as a key cause of "decline." Adorno thought he could be forgiven and profitably read, mainly critcising--again--his superstition, and possessive, bourgeois attitude towards culture: he wanted it all.

To put this into context, compare his work to Houston Stewart Chamberlain's Foundations of the 19th Century (a pretty mainstream book: George Bernard Shaw approved). He also takes a panoramic, passionate view of Culture, but one based wholly on pseudo-scientific ideas about race--tracing bloodlines, genealogies, bone structure, etc. (also using Goethe's organicism as a starting point). And, incidentally, tho also disavowing anti-semitism as immature, thinks Jews are one the most significant problems facing modern society, with an entire section on the many reasons why they are a pernicious influence on culture--through no real fault of their own, tho, god love em. it's just that cross-breeding doesn't work; discrimination is essential to a healthy society, and kicking them out is for their own good (anticipating the complicated relationship between the nazis and zionism).

Spengler is I think too idiosyncratic to be satisfactorily reduced to "views," however. His views are fundamentally stylized, an intense concoction of misanthropy and mysticism, and therefore must be judged mainly on the implications of his style (and consequently his influence has been mainly literary; although Kissinger apparently started out as a Spenglerian). He's probably less "racist" in his arguments--if only because more absurd--than most writers operating in so risky an area. Buckle, Gobineau, Toynbee...even Jared Diamond. He's a gothic symbolist, forming, in his peasant-like wonder, an essential link in the chain between Carlyle and Heidegger (not the most respectable company, admittedly).

I read Decline a few years ago now so I may have forgotten important things, and haven't read his other works. But here is a rather worrying description of a later polemical work "the hour of decision" by Allen Tate (someone with his own race problems):

Capitalism and Socialism are simply different names for an attack on the institution of property that has now been going on since the latter part of the seventeenth century. International finance-capitalism has attacked the ownership of land and has reduced even factory production to slavery; it is the attack from above. Socialism would carry this process further; it would destroy the last trace of private property and schematize the whole function of man in the abstract moneysystem invented by finance capital: this is the attack from below. It is a single attack, and those men who stand apart from it may be inclined to look upon the tragic illusion of difference between capitalism and socialism as the fatal argument of Tweedle-dum and Tweedledee. The argument of these amiable gentlemen Spengler calls the White World-Revolution. In the dim background supporting the White, there is the Coloured World-Revolution. The Liberal movement, says Spengler, has marched from Jacobinism to Bolshevism, and in the progressive abstraction of the moral nature of man into the purely economic function, the whole quality of cultural life is ignored: the "workers" everywhere in the world become abstract brothers. The integrity of Western culture, under the catchwords of Justice and Equality, is betrayed by an alliance with the Coloured Races. As European man loses his power of rule, the dark peoples rise to dispute that power. The end will probably be another Dark Age, a fellaheen society of economic slaves dominated by small groups who are themselves dominated by the extreme abstractions of moneycapital—a society without quality, roots, arts, or a conviction of the specifically human role.

Whether one can excuse this kind of thing depends upon how seriously you take him. whether you want to grant him "artistic license" or charitably take the Liberal movement to mean cultural imperialism, nation-building, etc.