What reasons did the racists/homophobes/sexists/etc give as their reasoning?
A summary of their point of view would be:
P1)Some are inferior
P2)You should treat others based on their value
C)You should treat some better than others
Now we would disagree with their first premise but it does not take a logician to notice that the argument is sound for those that accept the premises. Thus it would be unreasonable to claim these people are lying about what they believe or "know better".
I even met this point of view:
P1)Pain and suffering are good
P2)We should maximize the good
C)We should maximize pain and suffering
Suffice to say I vacated the premises quickly.
In conclusion: Not everyone sees the world as you do. As a result people can logically draw different conclusions from you without lying or "knowing better".