The polarization of fast radio bursts (FRBs), which are bright astronomical transient phenomena, contains information about their environments. Using wide-band observations with two telescopes, we report polarization measurements of five repeating FRBs and find a trend of lower polarization at lower frequencies. This behavior is modeled as multipath scattering, characterized by a single parameter, σ _RM , the rotation measure (RM) scatter. Sources with higher σ _RM have higher RM magnitude and scattering time scales. The two sources with the highest σ _RM , FRB 20121102A and FRB 20190520B, are associated with compact persistent radio sources. These properties indicate a complex environment near the repeating FRBs, such as a supernova remnant or a pulsar wind nebula, consistent with their having arisen from young stellar populations.