There are some good answers here. I'd like to just add that Racism was an integral part to (atheistic) Darwinism. The real title of his book on Origin of Species included the "Favored Races".

Christianity has always held true to its claims that we are all one.

I think any distinction a person makes between races where any race is marginalized, demeaned, undermined, or rendered inferior or any way is racism. But it could be that racism is just one of those words that's hard to define precisely, but you can generally recognize it when you see it.

Racism is the belief that any race is superior or inferior to another. This is clearly sinful per the creation account of Adam and Eve in Genesis 1:26. All people are made equal in God's image.

I have seen many Christian leaders denouncing the sin of racism (especially of late), but I have not seen any clarification of what this sin consists in, given that "racism" has been defined in myriad ways. If it means "hatred of another person because of their race", then it is clearly a sin, because hatred is, in itself, sinful.

So I shall use "racism" to mean "the belief that there are significant (according to worldly ways of judging) and non-superficial differences between various races." This excludes differences in melanin content, which are superficial, and differences in kidney function, which everyone regards as insignificant. However, it includes differences in long-distance running ability, which, however insignificant from a Christian standpoint, are considered significant by the secular world when the Olympics roll around. Is this form of racism sinful? More broadly, how should the sin of racism be understood?