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The entire Republican party is not racist -- any claim that suggests that is pretty laughable. However, the Republican party (since Nixon at least, when LBJ signed the civil rights act) has long had a strategy of, er, courting racists (though not as explicitly as Trump has).

https://en.wikipedia.org/wiki/Southern_strategy

To be honest, it's probably better to throw "racism" / nativism under the broader category of "right wing populism". Many other rich world countries do still have (to some degree or another) a pure right wing populist party that on some sides exhibits some racist / nativist / identity politics tendencies; since many of these countries are parliamentary and are not necessarily first past the post, they are often their own entity (eg National Front, UKIP, Party For Freedom, etc.).

The United States is not a parliamentary system (and uses a first past the post style method to boot); this results in more party integration. Thus the US only has two dominant parties, and both tend to be slightly uneasy coalitions as a result (that are not necessarily static; the Democrats and Republicans 60 years ago represented quite different things).