In today's world, the "challenge" of cultural diversity turns out to be the basis for further social processes and necessitates the reorientation of conventional cultural institutions of social life to the recognition of the possibility of different cultures to develop fully within a particular social community. Another problem is the search for a person's ability and capability to "protect" "his/her own self" in the face of the threat of unification and depersonalization of the globalized world, to choose the most personal thing to him/her in society. Evolution towards a multicultural world predetermines the search of productive methodological approaches in explaining the integrative processes of the modern world and outlining strategies for the development of cultural diversity and multicultural coexistence. An intersubjective approach is relevant and productive in this perspective of consideration. In philosophical discourse, intersubjectivity is understood as intersubjectness and implies a connection between subjects, not identical, not universal Ego-Ego, but rather individual, autonomous, equal Ego-Other, emerging and understood as unique existence world by virtue of their nature. The concept of dialogue is a kind of "solidarity" of the Otherness existences. The dialogue is seen as the goal and principal means of spiritual objective reality and renewal of modern social objective reality, demonstrating the ability to find common solutions, ways of understanding and harmony in resolving conflict situations, overcoming conformism and selfishness. A world deprived of cultural priorities in the development of certain cultures and the neglect of the opportunities and characteristics of others will deprive the human race of hostility and intransigence, will acquire the contours of a pluralistic, multicultural image, since it is "woven out" from the discourse of different value-worthy civilizational achievements.