Regarding the three kinds of "political modernities," what about modern Western society were anti-Western ideologies reacting to?
If the framework of your question is what is known by some as the three "epochs" of modernity, then you are being asked to examine anti-Western civilization ideological reactions against Western civilization (Mediterranean, European, British and, later, North American) during each of the three epochs. Professor Mitchell of Dallas Baptist University identifies these three epochs as Antiquity, Medieval and Modern. Others, like Central European University, define "political modernities" as ideologies holding sway between roughly 1860 and 1945.
A brief overview of some anti-Western ideologies relevant to Mitchell's epochs would include the opposition toward laxity in social stratification in the epoch of Antiquity. Anti-Western social stratification is well represented by the non-Western caste system in India. Anti-Western ideology in Antiquity also includes opposition to the absence of religious rigor relevant to social and political structure since the Greek and Roman pantheons did not hold political sway as religious structures did in non-Western civilizations. To illustrate, in non-Western civilizations, religion, like Hinduism, often dictated the political governance structure, like Japan's deified emperor, and the social caste or peasant structures. In the Medieval epoch, anti-Western thinking opposed Western Humanistic philosophical thinking as contradictory to religious philosophical thinking, like that of Confucius. In the Modern epoch, anti-Western ideology opposed individualism, as propagated by the Enlightenment and the revolutionary spirit, as contradictory to social group cohesion and the duty of stratified levels within society and families to higher stratified levels within society and families.
A brief overview of anti-Western ideologies between 1860 and 1945 would include some of the same ideologies that define opposition during the Antiquity, Medieval and Modern epochs. A useful example of anti-Western ideology in the social sphere is opposition to individualism in economic manipulation, for example by industry giants who reduced workers to interchangeable units, as being contradictory to collectivism and empowerment of the worker, as seen in Marxism. Another example is opposition to a-moral decadence and irreligious individualism, as illustrated by the then burgeoning film entertainment industry, as being contradictory to morality and devotion to higher laws stemming from fervor in religious commitment such as is seen across the globe presently between Jews, Muslims and Christians and in India between fundamental Hinduism and opponents to the caste and untouchability systems contained within Hindu religious doctrine.