[michaelmrose]

> as far as I understood recently about US is that the speech is protected between the citizen and the government, not between civil entities, as business/corps and citizen

Free speech by anyone to anyone is protected from government restriction. It is the government that is forbidden from punishing speech not the government that must be party to the speech else free speech would have nearly zero meaning.

> Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

What is oft said is that the first amendment doesn't protect you from non governmental consequences for your speech. For example you can be fired for your speech but you may not be imprisoned nor silenced by the government.

When a private entity avails itself of remedies provided by the government to limit or punish your speech your constitutional rights are infringed because it is the government acting to limit your speech even if its on behalf of a claimant.