Until recently, museums mainly communicated well-established knowledge. Current science, however, is characterized by a rapid knowledge increase, so that we often have to deal with fragile and inconsistent knowledge. In order to develop exhibitions that encourage visitors to process information in a differentiated way, museums need to know how visitors deal with conflicting information. Furthermore, museum professionals need information on personal and situational factors that may promote the processing of such information. We tested whether conflict processing is influenced by personal characteristics such as situational interest, epistemological beliefs, tolerance of ambiguity, and self-efficacy on the one hand and by situational conditions such as the spatial arrangement of information on the other hand. In two science museums and one museum of cultural history, text pairs were displayed that described a topic from conflicting perspectives. The spatial distance between the two texts was manipulated. Semi-structured interviews and questionnaires captured the personal characteristics of 323 visitors and the way they dealt with conflicting information. The results showed that a majority of the visitors perceived a conflict, and a large proportion was willing to process the information at a deeper level. Sophisticated epistemological beliefs, a high tolerance of ambiguity, and high self-efficacy were found to promote situational interest in conflicting information. High situational interest, in turn, promoted a tendency to process deeply. Placing text pairs in close proximity had a positive effect on the processing depth in science museums but not in the museum of cultural history. A possible explanation lies in the higher density of additional and potentially interfering information in the science museums compared to the museum of cultural history.