It all depends on what those differences are.
For eg: do they believe (like some on this board) that women are inferior beings? DO they believe in Allah/Mohammed instead of god/Jesus? do they believe the world is flat and man never went to the moon? and what are they using "my business" for? Is it to build RPGs to kill GIs in iraq? Are they using it in a negative way? Do they believe in segregation and are using my business to promote segregation?
If their core beliefs are benign in nature then I'd have no problem doing business with them. On the other hand if, using Nazis as an example, if they were promoting hatred and or violence then no, I wouldn't do business with them.