Owing to polarization-independent property of propagating phases inside isotropic dielectric layers, Fabry-Perot resonances in metal-dielectric-metal sandwich structures and one-dimensional (1-D) photonic crystals (PhCs) with isotropic dielectric defects are polarization-insensitive. Herein, we introduce an all-dielectric elliptical metamaterial (EMM) defect into a 1-D PhC to realize an anomalous polarization-sensitive Fabry-Perot resonance empowered by the polarization-sensitive property of the propagating phase inside the all-dielectric EMM layer. The wavelength difference of the Fabry-Perot resonance between transverse magnetic and transverse electric polarizations is larger than 100 nm at the incident angle of 45 degrees. Enabled by the polarization-sensitive property of the Fabry-Perot resonance, high-performance polarization selectivity can be achieved in a broad angle range. Our work offers a viable recipe, well within the reach of current fabrication technique, to explore polarization-dependent physical phenomena and devices.