Negligible I would say. All professional audio before digital put signals through dozens of opamps quite happily. You might want to checkout this thread of mine too: https://www.diyaudio.com/community/threads/12-opamps-chained-measurements.346722/
In fact the art of analog signal processing is in using enough active devices to correct for or avoid the failings of passive components, be it gain loss, impedance issues, noise, non-linearity (ie inductors, large value capacitors). This might seem counter-intituitive till you actually try doing design for real, for instance a low noise differential line-input circuit (where 3+ opamp designs out perform the single opamp considerably).