Among the several approaches that have been attempted at studying opinion dynamics, the Sznajd model provides some particularly interesting features, such as its simplicity and ability to represent some of the mechanisms believed to be involved in real-world opinion dynamics. The standard Sznajd model at zero temperature is characterized by converging to one stable state, implying null diversity of opinions. In the present work, we develop an approach—namely the adaptive Sznajd model—in which changes of opinion by an individual (i.e. a network node) implies in possible alterations in the network topology. This is accomplished by allowing agents to change their connections preferentially to other neighbors with the same state. The diversity of opinions along time is quantified in terms of the exponential of the entropy of the opinions density. Several interesting results are reported, including the possible formation of echo chambers or social bubbles. Additionally, depending on the parameters configuration, the dynamics may converge to different equilibrium states for the same parameter setting, which suggests that this phenomenon can be a phase transition. The average degree of the network strongly influences the resultant opinion distribution, which means that echo chambers are easily formed in systems with low link density.