  We adapt and extend the Montiel-Ros methodology to compact manifolds with
boundary, allowing for mixed (including oblique) boundary conditions and also
accounting for the action of a finite group $G$ together with an additional
twisting homomorphism $\sigma\colon G\to\operatorname O(1)$. We then apply this
machinery in order to obtain quantitative lower and upper bounds on the growth
rate of the Morse index of free boundary minimal surfaces with respect to the
topological data (i. e. the genus and the number of boundary components) of the
surfaces in question. In particular, we compute the exact values of the
equivariant Morse index and nullity for two infinite families of examples, with
respect to their maximal symmetry groups, and thereby derive explicit two-sided
linear bounds when the equivariance constraint is lifted.
