During C. elegans oocyte meiosis I, cortical actomyosin is locally remodeled to assemble a contractile ring near the spindle. In contrast to mitosis, when most cortical actomyosin converges into a contractile ring, the small oocyte ring forms within and remains part of a much larger and actively contractile cortical actomyosin network. This network both mediates contractile ring dynamics and generates shallow ingressions throughout the oocyte cortex during polar body extrusion. Based on our analysis of requirements for CLS-2, a member of the CLASP family of proteins that stabilize microtubules, we recently proposed that a balance of actomyosin-mediated tension and microtubule-mediated stiffness are required for contractile ring assembly within the oocyte cortical actomyosin network. Here, using live cell imaging and fluorescent protein fusions, we show that CLS-2 is part of a complex of kinetochore proteins, including the scaffold KNL-1 and the kinase BUB-1, that also co-localize to patches distributed throughout the oocyte cortex during meiosis I. By reducing their function, we further show that KNL-1 and BUB-1, like CLS-2, are required for cortical microtubule stability, to limit membrane ingression throughout the oocyte, and for meiotic contractile ring assembly and polar body extrusion. Moreover, nocodazole or taxol treatment to destabilize or stabilize oocyte microtubules, respectively, leads to excess or decreased membrane ingression throughout the oocyte and defective polar body extrusion. Finally, genetic backgrounds that elevate cortical microtubule levels suppress the excess membrane ingression in cls-2 mutant oocytes. These results support our hypothesis that CLS-2, as part of a sub-complex of kinetochore proteins that also co-localize to patches throughout the oocyte cortex, stabilizes microtubules to stiffen the oocyte cortex and limit membrane ingression throughout the oocyte, thereby facilitating contractile ring dynamics and the successful completion of polar body extrusion during meiosis I.