Line level means we don't need to worry about dealing with high currents, voltages or significant power dissipation (large packages are better at dissipating heat than small ones). But it also means that any distortion will be amplified by the following gain stages.
Setting the time constant means that we're attenuating a selection of frequencies, in this case ones we can hear so we're looking for precision and linearity (high linearity = low distortion).
If the actual capacitance deviates from the nominal capacitance then we'll find that the -3dB point is at a different frequency to that specified. In this case, assuming you can adjust the roll-off of your subs then the precision of the pair of filters (left and right) is not overly critical. However the precision between the filters (the difference between left and right) is critical and may well be audible if one channel rolls off at a different frequency to the other.
So we want to know that the capacitors on both channels are close in value but not so worried about how accurate that value is (in an RIAA filter both values are critical).
Linearity is a lack of distortion so the output of a linear component will closely resemble the input (in this case we are intentionally distorting the input by filtering out LF, but we want the audible frequencies to be unaffected). Linearity is measurable in Total Harmonic Distortion and there have been studies into the distortion characteristics of dielectrics, if you want to learn more (and I completely understand if you don't) Doug Self has researched the topic in depth. C0G/NP0 and polystyrene caps can be considered free of distortion, polypropylene is very low distortion which can probably be said to be negligible, electrolytic is another matter.
So bearing this in mind...
Jupiter Copper Foil: I don't know the linearity of wax and paper but it can't be better than unmeasurable, so let's be generous and assume it's unmeasurable. Precision... the ones I found were 5%, okay but not great.
Clarity CMR: These are polypropylene so we know what we're dealing with. Precision is 3% which is better.
Miflex KFPM: Polypropylene and 2% precision.
Audyn True Copper: Couldn't even find out what the dielectric is, so let's assume it's unmeasurable again. 2% precision.
I couldn't find (admittedly I didn't try too hard) any detailed datasheets for the above. One thing they all have in common is that they are large, which means they can dissipate heat (which we don't need) but the size also means that the parasitic properties of the leads, foils etc are greater.
Polystyrene is available in 1% in a small package and has no distortion to speak of. So it's not streets ahead of the caps above but it will be better for this application (and that's without taking into account cost). Some of the exotics will probably be available in matched pairs which is an improvement... but still not better unless the matching is less than 1%.
I wrote more there than I meant to... I hope it's useful.