Rural homestay inns are an important part of rural tourism, and tourists’ support behavior intentions are important factors affecting whether rural homestay inns can be developed sustainably. The local authentic life experiences and realization of actual communication between the host and tourists are the main influencing factors for tourists to revisit, recommend, or provide support. Although previous studies have confirmed the influence of authenticity perception on tourists’ support behavior intentions from different perspectives, they have not analyzed the influence mechanism between them from the perspective of micro interpersonal emotional attitude. To further understand the impact mechanism between the two, this study introduces the variable of emotional solidarity; constructs a relationship model of authenticity perception, emotional solidarity, and tourists’ support behavior intentions by adopting the theory of reasoned action; and verifies the established hypotheses through empirical analysis. The results show that both existential authenticity and objective authenticity positively influence tourism support behavior intentions, and the effect of objective authenticity on tourism support behavior intentions is greater than that of the presence of authenticity. Empathic understanding, feeling welcome, and emotional intimacy all play mediating roles between intrapersonal authenticity perception and tourism support behavior intentions. Findings also show empathic understanding and feeling welcome play mediating roles in objective authenticity perception and between the perception of objective authenticity and tourism support behavior intentions. Suggestions are also proposed for the development of homestay inn enterprises.