No mention of platform - if you're using a Pi or similar the answers will be a little different as for the moment I'm assuming PC of some sort.
A quick primer on the audio subsystems available in linux, and their use cases:
* ALSA - This is the kernel level sound interface, and the others sit on top of it. It has a powerful text-based config file that you can use to add a variety of filters and effects with - enough for an active crossover and more besides - but has no hand holding. A typo will stop it working with little or no explanation as to what's gone wrong. It has the least opportunity for strange things to happen once properly configured, and most applications can access it directly, but offers few of the nicities that people have come to expect from desktop audio, hence the need for the following layers.
* PulseAudio - used by most distros with a desktop gui to offer the nicities. There's a config option in more recent versions to avoid resampling unless it's necessary - without that set it will resample everything to a common format so that it can mix the inputs. If you're hot plugging audio devices (usb, bluetooth, network audio) there have been issues with it unexpectedly switching the output from one to another, allegedly fixed or at least improved in recent releases. It can use plugins for processing - you'd probably want to look at
Pulseaudio Crossover Rack as an easy way to do what you're after. It expects a logged in user, and by design doesn't play well with system level audio daemons.
* JACK - mostly used for audio production type situations. Has GUI stuff for building chains of audio processing applications, so an active crossover can be configured by GUI. Because of the chaining and mixing it operates everything at a fixed format as I understand it, so if you have sources with different sample rates and bit depths they're going to get resampled once, although with a decent resampler. Since many active crossovers operate at fixed rates anyway this might not be as much of a problem as you'd initially think.
* PipeWire - a relatively new development that distros may start changing over to within the next year or so but AFAIK not used by default in any of them just yet. The intent is to provide the capabilities of both JACK and PulseAudio, including compatible interfaces so that existing applications for either keep working with no changes necessary, plus similar facilities for video streams. It's not there yet, but getting close. Quite what this will mean for unexpected audio things I don't know, and it may still be a moving target
Probably avoid Gentoo or Arch - they offer the greatest ability to tweak things exactly as you'd like them with any of the above, but this can cause confusion if you don't know what you're doing. Their documentation is very good for the deeper technical details though, so if you're willing to put the time in to learn then it might not be so bad. Keep them in mind for the long term though.
An ordinary desktop distro like the various Ubuntu flavours, or Mint, will almost certainly be using PulseAudio by default. They should be an easy combination with PulseAudio Crossover Rack with little or no need to use the terminal. They're widely used so relatively easy to find advice on troubleshooting, but look for multiple sources that agree as the quality can be variable. You'll probably want to check the current suggestions for tweaking config options for best audio quality - mostly tweaks to resampling method last I looked - but by default they're usually not bad.
Ubuntu Studio (and its Fedora equivalent whose name I forget) are preconfigured to use JACK and have a load of filters available for assembling a crossover.
I think I'd still use some level of analog low pass (EDIT:
) to protect mid and tweeter in case something should go wrong, but I may be paranoid!
