  We present a method to engineer the frequency splitting of polarization
eigenmodes in fiber Fabry-Perot (FFP) cavities. Using specific pattern of
multiple CO$_2$ laser pulses, we machine paraboloidal micromirrors with
controlled elliptical shape in a large range of radius of curvature. This
method is versatile and can be used to produce cavities with maximized or
near-zero polarization mode splitting. In addition, we realize dual-wavelength
FFP cavities with finesse exceeding $40\,000$ at 780$\,$nm and at 1559$\,$nm in
the telecom range. We provide direct evidence that the birefringent frequency
splitting in FFP cavities is governed only by the geometrical shape of the
mirrors, and that the astigmatism of the cavity modes needs to be taken into
account for specific cavities.
