> I'm having trouble believing that most people making this argument normally promote free markets

I’m a staunch free marketer and First Amendment advocate. I think this is a freedom of assembly issue. Amazon should not be forced to assemble with these customers.

If anything, this same group has fought for a more extreme version of this freedom through its don’t-sell-cakes-to-gays schtick.

(To be clear, I support e.g. the Westboro Baptist Church’s right to speech. They say awful things. But they have the right to. If they started organising murders or lootings of gay-owned businesses, on the other hand, I would not consider their actions protected.)

I think an argument like this is consistent with free (i.e. few rules) markets. Isn't it the same argument as saying businesses should be allowed to refuse customers based on, say, sexual orientation? People may not agree with that and would want government to require businesses to serve some customers and, in this case, not others. However, I tend to think business and customer relationships should be voluntary as much as possible.