How can you know if the accusations are weak if you haven't bothered to look at the evidence supporting them?
No, that isn't the definition of racism, and there is nothing incompatible about racism and libertarianism, despite that awkward explanationyou attempted. You've made that point yourself in the point you made in #2 above. In a libertarian regime, an unapologetic racist would/should be able to deny use of his property to races he hates. So, someone could clearly be a rabid racist and a libertarian - you clearly support someone's free-born right to be a racist and exercise that racism through their private property.