The common-mode input capacitance of almost any OPAMP will be voltage dependent, because the reverse-biased isolation junction around the input devices acts as a varicap diode: as the voltage changes, the width of the depletion region changes, changing the capacitance.
One solution to this is to bootstrap the OPAMP supply rails so the common mode input voltage with respect to the supply rail does not change as the input voltage changes. You can use the output of the OPAMP itself, suitably level-shifted, to drive suitable fast voltage regulators (or even just emitter followers may be good enough). In theory, you only need to bootstrap the rail to which the isolation junction is connected, but it is often difficult to find out which that is, and if you do find out you still have the issue of maximum supply voltage to worry about.
Bootstrapping also effectively removes the common mode input capacitance - well a good part of it, anyway, in practice. There is still the differential input capacitance, probably dominated by the OPAMP package. Your bootstrap needs to have the full circuit bandwidth, of course.