Do you think someone should be able to sue a business for bias?

NO. They CAN, but should not be able to do so.

The business owner has AS MUCH right to be biased as you think you have to be treated fairly.

So businesses should also be able to refuse service based on race, religion, etc?  

When a business discriminates against a legally protected class, yes, I think members of that class have every right to sue.

The courts agree.

Would you feel the same if the unwanted customers were a different protected group? What if they wouldn't sell your wife a cake because she's a woman?

The Constitution didn't give the federal government the power to force private businesses to conduct business with people they don't wish to, regardless of reason.

But it is absurd that it is only wrong in some cases, depending on who is refused service and the reason they're refused service.  It's not the act of refusing service which is tortious, because in most situations it is perfectly ok.  

To me, this is ridiculous.  Either businesses can or they cannot refuse service.

If a black caterer can refuse to supply food to a KKK meeting, I cannot see that as being any different than a Christian baker refusing to bake a cake for a same-sex wedding.

This sounds just like Jim Crow laws, where businesses were forced to treat people differently.

Yes I think they should be able to sue.

And yes I think learned law scholars (judges) shall decide these cases based on their expert knowledge of the details of the case and also of the law as it applies.

Things get difficult and messy in America when one person's rights infringe upon another's rights.  There are no obvious clear-cut answers in many cases and this is why we have a civil justice system.

If you want to live in a country where you are not allowed to bring your grievances to court for a fair hearing by a judge, perhaps you would prefer North Korea or Saudi Arabia.

By the way, the bakery owners weren't sued for their biased thoughts.  They were sued for behavior.   Two very different things.    No one made the argument that people aren't entitled to their opinions/biases and that we should have some kind of Thought Police.