As a comment on the post notes, Shopify already "censors" certain viewpoints. From their TOS:
"We may, but have no obligation to, remove Store Content and Accounts containing content that we determine in our sole discretion are unlawful, offensive, threatening, libelous, defamatory, pornographic, obscene or otherwise objectionable or violates any party’s intellectual property or these Terms of Service."
So they're actually saying "We don't find Breitbart violating the moral code as set in our TOS". This is not about free speech.
"We may, but have no obligation to, remove Store Content and Accounts containing content that we determine in our sole discretion are unlawful, offensive, threatening, libelous, defamatory, pornographic, obscene or otherwise objectionable or violates any party’s intellectual property or these Terms of Service."
So they're actually saying "We don't find Breitbart violating the moral code as set in our TOS". This is not about free speech.