IMO racism is only an adequate term when we have a pre-concieved notion at hands which is about genetics / a trait given by birth and which a group x shares.
If a pre-concieved notion is rather "merely" about cultural traits - than racism is the wrong word.
Except that human races have precious little to do with genetic differences.
Taxonomically, a race is a subset of a species that shares within that race genetic similarities where such similarities are sufficiently different from other members of the species to set the race apart from other races or subspecies. You've said as much.
However, the application of the term to the human population is flawed. Humanity exhibits just as much genetic diversity within its "races" as it does between the races. Indeed, it is not unusual for a group within a race to be more similar, genetically speaking, to a group within another race than a group within the first's own race. Such is the case with Italians, Irish, and black South Africans. The Irish, as a population, are more genetically similar to black South Africans than they are to Italians despite Italians and Irish both belonging to the same "race."
If you are going to start from first principals, as you appear to, then you should acknowledge that human races are purely a social classification and not a genetic one. Or, at the least, not have genetics enter into the discussion.
Whether or not this invalidates the rest of your argument is left as an exercise to the reader, but you should be aware that your initial facts are fundamentally flawed.
I, for one, agree that "race" and "racism" should not be used to describe purely social discrimination. In its place, I advocate nouns and adjectives based on ethnicity and other clearly social terms.