There's more factors in play, too. It's coherent to think B && !A, but also (C) Unelected members of the press should not have the power to shame businesses into excluding individuals and organizations.
No, you shouldn't have that power. Doing business with someone and providing services to them isn't and shouldn't be an endorsement of their values. Jeffrey Epstein should be able to hire whatever legal council he wants, convicted sex offenders should be able to find an apartment upon release, gun stores should be able to take credit card payments, and generally speaking you shouldn't get excluded from the benefits of modern society simply for being unpopular, no matter how just the reasoning.
One doesn’t elect employees of a private business. They choose not to consume media that business produces. Do you think that we should elect people to tell us what’s happening?
No, I'm saying that people generally should not use their influence with third parties to enact extrajudicial punishment. Tortious interference with contract is a bad thing.
So long as the WWW is a public network ran by private entities, essentially every decision is extrajudicial. I completely see the issue you're trying to highlight, but it seems that limiting the abilities of reporters and activists isn't healthy for democracy. If the services CloudFlare and others provide is regulated like a public utility, then standards like guaranteeing equal access regardless of ideology, or enforcing standards that have been democratically adopted. Is there a middle ground between regulation and corporate discretion in all matters of speech on that use their platform?