What are some examples of the variation in the answers of the same question among different researchers, that can be explained by the variation of epistemological and ontological grounds of their research methods?
An quick easy example is the study of exchange from Marcel Mauss to Claude Levi-Strauss to someone like Eduardo Viveiros de Castro:
1) Mauss operating with positivist epistemology of "social facts" influenced mostly by Emile Durkheim whose methodology is largely that of Comte.
2) Levi Strauss operating with a structuralist ontology of "social facts" influenced largely by things happening in linguistics like Ferdinand de Saussure and Roman Jakobsky, Malinkoswkian functionalism and Hegel.
3) Viveiros de Castro operating with a post-structuralist ontology of "social facts" influenced primarily by Levi Strauss, Marilyn Strathern and Gilles Deleuze.
Three perspectives on the same "social fact" of exchange in the primitive cultures come out with vastly different observations about the nature of the social facts under observation.
1) Mauss sees in exchange the presentation of gifts and counter-gifts and sees in this practice something common to all human societies
2) Levi-Strauss sees in exchange in primative societies solely exchange, discounting the subjective presentation of experience to arrive at a "theory of indigenous reality" not to be found in the perspectives of the indigenous themselves
3) Viveiros de Castro sees in exchange neither gift nor exchange (in any traditional sense) but always a transformation of the parties that come together for the "transaction", a transformation for mututal survival. And he also sees in the analyses of the anthropologist not impartial observers relating the facts and tales of natives, but participants in the transformation of facts and tales that are no longer what they were to the natives.
The ontological and epistemological presuppositions of each are radically different, and changing sometimes consciously because of philosophical influences (i.e. Viveiros de Castro) but more often from influences from the field of study itself. Unspoken presuppositions. They also each have evolving relationships with science. Mauss and Levi-Strauss both attempting in their own way to provide methodological precision to their "sciences". Viveiros de Castro taking a step back at the recognition of major flaws in the reductivism and non-impartiality of the previous two anthropological or sociological perspectives.
To the question "how do these people live?" the answers are relatively similar, but to the question of "how do these people see and understand their world?" or put differently "what is the world and reality lives by x population" the answers could not be more radically opposed to each other.
I use these three anthropologists just as examples because of both their popularity, but they are representative of three large movements/shifts within the field of anthropology itself since the mid-1800's to present that mirrors dozens of other well known anthropologists in their orbits.
An example I can think of is the different approaches to the ethnological studies of the late 19th century by Sigmund Freud (in Totem and taboo) and Elia Kaneti in (Mass and authority).
The same writers also derive different ideas about the case of the "judge Schreber".
For an explicit distinctions of epistemic and ontological senses of the objective and subjective (as well observer independence & observer relativity), see the articles referenced here