Pathologic Wnt/β-catenin signaling drives various cancers, leading to multiple approaches to drug this pathway. Appropriate patient selection can maximize success of these interventions. Wnt ligand addiction is a druggable vulnerability in RNF43-mutant/RSPO-fusion cancers. However, pharmacologically targeting the biogenesis of Wnt ligands, e.g., with PORCN inhibitors, has shown mixed therapeutic responses, possibly due to tumor heterogeneity. Here, we show that the tumor suppressor FBXW7 is frequently mutated in RNF43-mutant/RSPO-fusion tumors, and FBXW7 mutations cause intrinsic resistance to anti-Wnt therapies. Mechanistically, FBXW7 inactivation stabilizes multiple oncoproteins including Cyclin E and MYC and antagonizes the cytostatic effect of Wnt inhibitors. Moreover, although FBXW7 mutations do not mitigate β-catenin degradation upon Wnt inhibition, FBXW7-mutant RNF43-mutant/RSPO-fusion cancers instead lose dependence on β-catenin signaling, accompanied by dedifferentiation and loss of lineage specificity. These FBXW7-mutant Wnt/β-catenin-independent tumors are susceptible to multi-cyclin-dependent kinase inhibition. An in-depth understanding of primary resistance to anti-Wnt/β-catenin therapies allows for more appropriate patient selection and use of alternative mechanism-based therapies.