I have been reading about Fascism from various expert sources, presently Professor Roger Griffin's Oxford Readers book Fascism. From this, and other sources (Robert Paxton, Stanley Payne, etc) we can identify commonality in belief and practices between Italian, German, and Spanish Fascists. This is not the same as saying merely a member of the regime, which is not the subject of this question.
We are explicitly discussing Fascists, as defined by world experts and not laypersons.
We are also discussing the history of eugenics, and what ideas inspired those differences in terms of the history of science (which contains many ideas, few of which turned out to be scientific.)
I discovered that Falangism, at least, the explicitly Fascist elements instead of the merely Francoist members, were racist but believed in creating a "Hispanic supercaste" via race mixing that is "ethically improved, morally robust, spiritually vigorous".
In comparison, one BBC documentary The Nazis: A Warning From History (episode 4 The Wild East), mentions one argument between senior Nazis over the question of racial purity.
Albert Forster, who was responsible for Danzig West Prussia, though a committed Nazi did not believe in Nazi racial ideas. He decided that the fastest way to "Germanise" his part of Poland was to grant German citizenship to as many Poles as he could, without checking their ancestry. This infuriated his neighbouring governor: Arthur Greiser, a fanatical racist. Greiser wrote a letter of complaint to Heinrich Himmler, who then sent an irate letter to Forster:
"You as a National Socialist know that just one drop of false blood that comes into an individual's veins can never be removed."
Forster however ignored the letter, joking that someone who looked like Himmler shouldn't talk about race so much. And Hitler, having a hands-off approach to government, never intervened: allowing governors to handle their domains as they liked.
As far as I understand it, the Nazi establishment practised negative eugenics (removing undesirable traits). This contrasts sharply with what I understand of Falangist eugenics, which was mostly positive (promoting desirable traits).
Most Spanish Fascists regarded race mixing as part of a civilising mission, to spread good genes, while most German Fascists regarded race mixing as a threat, which would damage good genes.
Why were German Fascist so obsessed with keeping the master race pure? While their Spanish peers were confident that the Spanish race could produce superior hybrids? And where did Italian Fascists stand on the issue?
It seems like German Fascists adopted a theory of race inspired by the Scientific Racism of Francis Galton, which appears to have been focused on negative eugenics. But I don't understand where the Spanish Fascists were getting ideas which led to the opposite conclusions about race mixing.