Like coils, all capacitors represent an energy storage.
When a capacitor is connected in parallel to a loudspeaker something else happens. If the voltage to the loudspeaker needs to change, the capacitor must be recharged first. The capacitor prevents quick voltage changes, therefore passing on only low frequencies to the loudspeaker.
Therefore: lossy capacitors don't let the current pass through unhindered at high frequencies since the terminals represent an ohmic resistance. Besides, they are not insulating at lower frequencies, because the insulator shows a measurable conductance.
Additional important notes: If a crossover is optimised for a low quality capacitor, the use of a high quality capacitor often doesn't show any advantage. The crossover needs to be tuned again incorporating the high quality component.
Example:
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