They aren't.

 They are deciding what YOU purchase from THEIR private company.

 Read whatever you want.

"So a private company, can determine what is purchased from that private company,
unless that Private company is baking/decorating something."

 No.  But you already know that.

 Not every company has to follow a singular set of laws.  Each State has versions of laws and there are federal laws.  So Amazon does not have to meet State requirements for equal creation of goods, until they open cake shops in States that will hear discrimination cases.

 But you can read whatever you want.  That's the defense you asked for.

 I think this might be something along the way things worked out for Nike.

 They took the Kaepernic stance and lost a ton of customers, but gained by simply being able to claim they were ahead of the BLM movement.  This value is strong by comparison and they now have a larger customer base.  Even on this forum it was predicted Nike would fail, but in Jan they had an all-time high.

 So is it beneficial for Amazon to pull certain books?  I imagine so and I imagine they have an astronomical data set to evaluate the impact of each book.  They will probably get more customers by pulling pro-Nazi books than by keeping them, and they will certainly use less resources defending this decision than defending why they are keeping them.  Social media relations alone would justify the cost.  

 But at the end of the day Amazon is not telling you, or deciding for you what you can or can not read, they are only deciding what you can buy from them.  But by spinning it we can maybe convince people that don't know what "rights" actually are that Amazon has this power.  But then there's the challenge of getting people to think they can not read something that isn't on Amazon.  At that point the spin gets revealed and people start to realize it's nothing more than complaining.

 Essentially it's our responsibility to stop using Amazon if we do not agree with their business practices.