It is generally accepted that the symmetry-protected quasi-bound states in the continuum (qBICs) are induced by breaking geometry symmetry in the regular quasi-planer nanostructure. However, it is very challenging to allow precise control of the asymmetry parameter in the process of fabrication and realize a tiny tailoring geometry symmetry. Here, a novel permittivity-asymmetric membrane metasurface, which can also induce polarization-insensitive qBICs by a symmetry breaking in the permittivity of the comprising host and guest medium is proposed and investigated. Simulation results show the line width and spectral position of resonances can be controlled by increasing or decreasing the refractive index of the guest medium. The far-field multiple decompositions and the near-field distributions reveal the physical mechanism of dual qBIC modes, which are dominated by the magnetic dipole and toroidal dipole and display opposite optical properties. Furthermore, it is found that such BICs are robust against the shape of the guest medium. Eventually, the sensing performance of the proposed structure is evaluated. This study provides a simple and promising structure for the excitation of qBICs and conceives a feasible approach to achieving a high Q factor.