This paper constructs a two-party evolutionary game model based on the perspectives of sharing platforms and consumers, exploring the dynamics of platforms’ decisions to actively operate with blockchain technology and the evolution of consumer rights protection behaviors. It is discovered from analysis that certain variables exert considerable influence on the stability of the strategies of both parties. From the consumer perspective, the improvements in the performance of the blockchain technology significantly increase the consumers’ willingness to protect their rights: the consumers with initially high levels of rights protection activation intensified their actions when their rights were violated. Thus, with the effective reduction of the cost of safeguarding rights, this trend has been additionally strengthened. As for the platform side, the performance of the blockchain technology exerts positive incentives on the operation of the platforms, although the marginal impact gradually declines with the developing blockchain technology, which in return reveals that platforms need to pay attention to a range of aspects including technology maturity. Measures of dual constraints including heavy fines from government and negative impacts of passive operations help to rein in passive operation among the platforms. Significantly, higher values of fines or negative effects lead to higher tendencies of having proactive operation strategy among the platforms.