Nucleosynthetic isotope anomalies in meteorites allow distinguishing between the noncarbonaceous (NC) and carbonaceous (CC) meteorite reservoirs and show that correlated isotope anomalies exist in both reservoirs. It is debated, however, whether these anomalies reflect thermal processing of presolar dust in the disk or are primordial heterogeneities inherited from the solar system’s parental molecular cloud. Here, using new high-precision 84Sr isotope data, we show that NC meteorites, Mars, and the Earth and Moon are characterized by the same 84Sr isotopic composition. This 84Sr homogeneity of the inner solar system contrasts with the well-resolved and correlated isotope anomalies among NC meteorites observed for other elements, and most likely reflects correlated s- and (r, p)-process heterogeneities leading to 84Sr excesses and deficits of similar magnitude, which cancel each other out. For the same reason there is no clearly resolved 84Sr difference between NC and CC meteorites, because in some carbonaceous chondrites the characteristic 84Sr excess of the CC reservoir is counterbalanced by an 84Sr deficit resulting from s-process variations. Nevertheless, most carbonaceous chondrites exhibit 84Sr excesses, which reflect admixture of refractory inclusions and more pronounced s-process heterogeneities in these samples. Together, the correlated variation of s- and (r, p)-process nuclides revealed by the 84Sr data of this study refute an origin of these isotope anomalies solely by processing of presolar dust grains, but points to primordial mixing of isotopically distinct dust reservoirs as the dominant process producing the isotopic heterogeneity of the solar system.