If you have an active crossover and also a protection cap, then you still have a passive filter in the speaker circuit. Protection capacitors are first-order filters. There are reactive components in the loudspeaker circuit, so care must be taken to ensure you don't reduce the benefits afforded by bi-amplification.

There are a couple of things that can be done, and both amount to the same thing - Check for peaking and remove it.

One thing you can do is to put a very large protection capacitor in series, so that the peaking would be at a very low frequency, far below the useful range of the transducer. But this has a couple of downsides. First is that this will move the peaking down to a low frequency, where a power-on "burp" might be the most harmful. And second is that the larger value capacitors get expensive, especially in the good film/foil technologies. Still, these are things that can be resolved and the use of a large protection capacitor is a good solution to the peaking issue.

The second thing that can be done is to use a damper resistor across the capacitor. This has the advantage of potentially allowing the use of a smaller capacitor. This, in turn, gives more confidence that a power-on surge will be removed or at least presented at a frequency that the transducer can handle. You can even use a protection capacitor configured as a crossover filter at the same frequency as the active crossover, effectively making another node.

Probably the best thing to do is to make a quick Spice analysis of your speaker circuit to find out how much effect there will be from peaking. You may find that your best solution is one that has a damper and a fairly large capacitor, or you may find peaking is so minimal that it almost doesn't matter. But to know for sure, you'll want to run the numbers and see.