in rephase, it is possible to make both, I tried both, but not sure what filter type is best.
The appeal of FIR-filters is that you can easily create linear phase filters, or in general just manipulate amplitude and phase independently, while for minimum phase filters both are linked. Loudspeaker drivers are minimum phase devices, so if you equalize their amplitude response with minimum phase filters, you will automatically linearize their phase response, so that would be the recommended way to go. By the way, I would implement the minimum phase part of the filtering with the biquad (IIR) filters in HFD.
For the crossover it's different, here the minimum phase filters will introduce phase shift, while linear phase filters avoid that. However, it's not easy to decide which is better. Minimum phase will introduce phase shifts and thus a 'bad' looking impulse response. BUT while FIR-filters can be better from a signal theory standpoint and produce a better looking IR, they don't necessarily sound better. At least there's lots of discussion going on about that on this forum and in general.
Problem with FIR is, that they introduce pre ringing which is not masked as much by the human hearing compared to the ringing of causal IIR filters. If that becomes audible is mainly a matter of your crossover slopes but can be influenced by many things.
