The Nazi ideology is what we call "Social Darwinism," which is to say, it is a specific application of ideas that are often associated with Darwinism (but not necessarily advocated by Darwin himself, and not necessarily actual consequences of Darwin's theory) to society. They believed in a hierarchy of races, which Darwin sort of does at times (though in much of his writings, he doesn't really even believe in race as a useful biological concept — he is contradictory on this point), but is an idea that well-predated Darwin. It is about the struggle for survival, but that idea has non-Darwinian versions and antecedents as well. So that is about as close of a "through-line" you can do from Darwin to the Nazis — a sort of gauzy inspiration, maybe, but even that is pretty round-about in practice.

Hitler, from what we can tell, never quoted Darwin or wrote about him one way or another. In Mein Kampf he talks about the struggle for survival, but again this can come from many sources, and he did so in particularly political (not biological) contexts. He speaks not of "evolution" but "development" (Entwicklung), which hints as non-Darwinian origins for any biological notions he has. The one writer on biology he quotes is Houston Stewart Chamberlain, a racial theorist who was anti-Darwinian.

Were there Nazis, in general, who believed in Darwinism? Obviously — there were hundreds of thousands of Nazis, including very good biologists and scientists. But it does not appear that there were any Nazi dictums about how one needed to feel about Darwin, nor whether it needed to be taught (or not). The Nazi biological interest was in "racial hygiene" (Rassenhygiene), which was eugenical in nature, and one can trace that intellectually back through Darwin (and many other thinkers), but it is not the same thing as citing Darwin or talking about strictly Darwinian evolution (as opposed to, say, Lamarckian evolution). There were also Nazis who explicitly rejected Darwin as overly materialistic. If anything, the most ardent Nazis appear to have rejected Darwin in favor of more gauzy theories of human development that prioritized the things they cared the most about (race, spirit, etc.).

So the connection between Darwin and the Nazis is pretty complicated and not at all direct. There is an excellent article by the historian Robert J. Richards which goes over all of the above, and goes into some of the details about how Nazi officials talked about Darwin when and if they ever did: Robert J. Richards, "Was Hitler a Darwinian?", which appears to be taken from a collection of essays on the same topic. There are, of course, some historians who claim the connection between Darwinism and Nazism was very close and tight — these claims appear to be quite ideologically motivated (often by Creationists), and rely on some unfortunate "tricks" to make the argument (like mistranslating the Nazis to make it look like they are talking about evolution more than they actually are). More common amongst reputable historians is a sort of vague intellectual lineage that moves you from Darwin through thinkers who did influence the Nazis (like Robert Proctor in Racial Hygiene, which is an excellent book about physicians under the Nazis, and has a sort of "intellectual history" of the Rassenhygiene movement in the beginning of it, which does include references to Darwin), which is valid, but Richards makes the excellent point that even these kind of fail if you look specifically at what the Nazis did advocate about evolution, which was often non-Darwinian (again, because of their anti-materialist philosophical streak).