Private businesses yes, but using many of those reasons as the sole basis to not provide service to a customer could earn a private business a lawsuit and/or government fines for violating various local, state, and Federal laws. The Federal Civil Rights Act covers "folks of different colors" and the Americans with Disabilities Act covers "those who appear to be crazy", and on the state level California's Unruh Civil Rights Act covers "gay folks" (and several other states have similar laws).
I'm pretty sure those laws only apply within the borders of the US. I'm not even sure they additionally apply to US-based companies doing business elsewhere...i.e., I don't think a woman in Saudi Arabia can sue Microsoft for gender discrimination under US law if they don't hire her. By the same token, countries that have more stringent laws would apply them to local hiring, service, etc.
The more I think about this, I'm pretty sure you can deny based on country simply by saying you don't serve that market. A business is under no obligation to serve all countries - you can simply say you lack the expertise (linguistics, culture, etc.) for that market and have made the decision not to accept orders from country X.
Disclaimer: IANAL.
And @
drmike, what's with the anti-Semitic bullshit? You're quoting one man who was not an elected leader of Israel, shooting his mouth off 40 years ago. I can find you lots of kooks to quote if you want to start bashing entire ethnicities based on one individual.
If you seriously believe Israel intentionally bombed the USS Liberty then you are at odds with virtually every historical account and the US government itself, which not only concluded it was clearly a mistake but later released NSA tapes of the Israeli pilots' conversations which make it very obvious. Israel had zero motivation and probably wet its pants at the mistake, later paid compensation, apologized strenuously, etc.