Ideologically different alternative media define themselves in opposition to mainstream journalism, and attacks on the perceived lack of objectivity of its authors are especially common for them. This paper examines their role in the context of Habermasian concept of the public sphere and distinguishes between alternative media as institutions of the counterpublic or antipublic. It also presents a proposal for a typology of contemporary attacks on journalistic objectivity (emancipatory, postmodernist, populist) and analyzes their main features in mo-re detail. On the basis of standpoint theory, we conclude that members of counterpublics, due to their strategic position in society, have a unique potential for constructive emancipatory critique, which can reveal that an apparently objec-tive stance represents only the perspective of the dominant class. Concerning postmodernist and populist attacks, we, on the contrary, draw attention to the fact that these are purely antagonistic positions misused for political propaganda, especially by the representatives of the right-wing populism movements constituting an antipublic rejecting the norms of rational democratic discourse. Postmodernist critique describes objectivity as a myth and resigns on its pursuit in advance or makes demands for public broadcasting to present various perspectives without considering the criteria of truthfulness. Populist criticism of the alleged liberal bias of the mainstream media relies in turn primarily on evoking negative emotions, misinterpretations of various notions (e.g., censorship, fake news), and paranoid condemnation of elites or expert knowledge.