Funny how similar argument is used by white nationalists to assert that they have a right not to do business with minorities. The mindsets of far left and far right are oddly similar.
You are walking around one day when you overhear someone accosting someone else. You run over to witness the accoster shouting vicious racial, religious, and/or sexual epitaphs at the accosted. You interrupt them and ask what's going on. It's clear the two don't know each other, and the accosted, who seems in shock, says he/she was just going about his/her day when this person noticed something about his/her appearance and started screaming. The accoster does not dispute this, and indeed, as soon as you've stopped asking questions, resumes accosting.
If you respond to this situation by any action (other than smiling and walking away or joining in the accosting), you are demonstrating intolerance for the accoster. Even simply trying to reason with him/her about his/her beliefs demonstrates some level of intolerance. But you feel sympathy for the accosted, you don't share the views of the accoster, and you want to help in some way. This is known as the paradox of intolerance and it's a challenging philosophical issue.
The argument against Shopify that is being made here is that the behavior and actions of Breitbart and similar groups and publications bring about an atmosphere that leads to intolerance towards minorities. Or, if you prefer something more concrete, a store in Indiana refusing to sell a wedding cake to a gay couple demonstrates intolerance towards homosexuals. What can we do to help or make them stop being intolerant? How can we respond to this intolerance without demonstrating intolerance ourselves? Or is intolerance of intolerance a moral obligation?
These examples just show that 100% tolerance, or tolerance of all ideas, equally, is a fairly tale proposition, not practical, and not conducive to well-functioning society. I like the concept of fuzzy-tolerance: try to understand where the accoster is coming from. Maybe some of his ideas have merit, while clearly others do not. Society should be in a constant tug-of-war, or re-negotiation, between tolerance of some ideas and intolerance of other ideas. The same thing happens, on a smaller scale, in your own mind.
Well, it's a fact whichever side uses it: refusing to do business with someone is not, by definition, censorship. In which cases it's right or wrong is a matter for debate, but it doesn't serve that debate to incorrectly call it censorship in order to benefit from the stong negative connotations of that word.
ANTIFA stands for the elimination of fascists, i.e. people who want to exterminate minorities.
BLM stand for bringing the police who shot notably innocent black people to justice.
Richard Spencer and the Fascist-Right have openly proposed and spoken in great depth about the sterilization and or extermination of PoC, Jews, etc. and how exactly to achieve it.
BLM leadership condemned the shooting. Googling "BLM + racism" mostly results in opponents of BLM calling them racist without backing up their arguments.