Two-dimensional (2D) insulators are a key element in the design and fabrication of van der Waals heterostructures. They are vital as transparent dielectric spacers whose thickness can influence the photonic, electronic, and optoelectronic properties of 2D devices. Simultaneously, they provide the protection of active layers in the heterostructure. For these critical roles, hexagonal boron nitride (hBN) is the dominant choice due to its large bandgap, atomic flatness, low defect density, and encapsulation properties. However, the broad catalogue of 2D insulators offers exciting opportunities to replace hBN in certain applications that require transparent thin layers with additional optical degrees of freedom. Here, we investigate the potential of single-crystalline molybdenum oxide (MoO3) as an alternative 2D insulator for the design of nanodevices that require precise adjustment of the light polarization at the nanometer scale. First, we measure wavelength-dependent refractive indices of MoO3 along its three main crystal axes and determine the in-plane and out-of-plane anisotropy of its optical properties. We find that the birefringence in MoO3 nanosheets compares favorably with other 2D materials that exhibit strong birefringence, such as black phosphorus, ReS2, or ReSe2, in particular in the visible spectral range, where MoO3 has the unique advantage of transparency. Finally, we demonstrate the suitability of MoO3 for dielectric encapsulation by reporting linewidth narrowing and reduced inhomogeneous broadening of 2D excitons and optically active quantum emitters, respectively, in a prototypical monolayer transition-metal dichalcogenide semiconductor. These results show the potential of MoO3 as a 2D dielectric layer for manipulation of the light polarization in vertical 2D heterostructures.