OK, now we’ve got that out of the way, here’s why:
As a political philosophy libertarianism is based on the view that all individual humans are worthy of respect, and that their actions should not be subject to the coercive interference of another without just cause. Now, what counts as “just cause” is open for debate. But it’s clear that if we truly believe that all individuals are worthy of respect then the mere fact that someone has a particular ancestry wouldn’t justify treating her differently from anyone else. (Nor, incidentally, would the mere fact that someone is a different sex justify her differential treatment.) If you believe that it does then you’re treating persons primarily as tokens of types of people, and not primarily as individuals. And that’s just not an individualist–or libertarian–view.
This doesn’t mean that you or your business are required to deal with types of people you don’t like. You can refuse service to anyone, on any grounds. But, if you do it solely on the grounds that they’re (e.g.) a Jew, or Irish, or a woman, then you’re not committed to treating people as individuals. And it’s that commitment–and not the view that you should not aggress against others–that is the fundamental basis of libertarianism. This is because the commitment not to aggress stems from the recognition that other persons are individuals with their own projects that you should not interfere with without just cause. The respect for individuals comes first; the duty not to aggress comes second. This means that the argument that a desire to refuse service to persons on the basis of their ancestry (or sex) is compatible with being a libertarian as such a refusal is simply the refusal to confer a benefit and not the infliction of a harm cuts no ice. It’s correct that a refusal to truck, barter, or trade is the refusal to confer a benefit and not the initiation of aggression. But if this refusal stems from treating one’s prospective trading partner as a token of a type of people rather than as an individual in her own right then it will be incompatible with libertarianism. Again, this doesn’t mean that it would be disallowed in a libertarian society. But the person so refusing would not herself be a libertarian–no matter how much she might agree with free markets, the non-aggression principle, or other doctrines associated with libertarianism.
So, no, you can’t be a racist or an anti-Semite and a libertarian. But libertarianism can (reluctantly) allow you to practice your racist or anti-Semitic views, provided that these are limited to withholding benefits and not inflicting harm.