What is meant by "civil society" in this article?
Civil society can be understood as the "third sector" of society, distinct from government and business, and including the family and the private sphere. By other authors, civil society is used in the sense of 1) the aggregate of non-governmental organizations and institutions that advance the interests and will of citizens or 2) individuals and organizations in a society which are independent of the government.
It does not. You are conflating:
civil 2b: adequate in courtesy and politeness : MANNERLY
with
civil 4: of, relating to, or involving the general public, their activities, needs, or ways, or civic affairs as distinguished from special (such as military or religious) affairs
https://www.merriam-webster.com/dictionary/civil
You can see that 'uncivil' does not include in its meanings an antonym of civil 4: