Laser-plasma accelerators (LPAs) now routinely produce electron beams with GeV energies over acceleration lengths on the order of a few centimeters. This capability and the demonstration of multistage coupling make LPAs promising for numerous applications. However, beam quality preservation in multistage accelerators remains an obstacle because of the need to separate the laser pulse from the electron beam. Plasma mirrors can be used to redirect the laser pulse, but their substrate thickness threatens to substantially degrade the electron beam emittance. Ultrathin (∼20 nm) liquid crystal (LC) plasma mirrors are an excellent candidate to address this challenge. This work investigates the robustness of thin LC plasma mirrors in the presence of capillary discharge plasma and an auxiliary heater laser. We find they can be operated ∼10 cm from the capillary exit when a heater laser is used. We then performed a normalized emittance measurement enabled using a 20 nm LC plasma mirror to protect electron beam optics after the LPA. The emittance contribution from scattering through the plasma mirror is calculated to be of order 100 nm, much less than the measured emittance of 4.0 μm. Finally, we develop a model to calculate plasma mirror performance based on the laser polarization and intensity, and plasma mirror thickness.