This looks like a design mistake. As you correctly noted, you can't build something where "something 50Ω connected or not" makes no difference to matching.
Your phrasing
dual antenna Wi-Fi module from Aliexpress
at least suggests you're also suspicious of the design quality.
If we assume the circuit is matched when no external antennas are connected, is it correct that connecting them will ruin the matching?
I honestly don't see how such a matching would look, but we can assume that the open connector simply acts as (bad) antenna, with a lot of reflections, and the rest of the energy leaves through the PCB antenna. That is a very optimistic assumption. More realistically, someone slapped these on the board, tried it and said "good enough".
If I connect external antennas permanently, with no intent of ever using printed ones, do I need to cut traces after the sockets to improve RF matching?
Impossible to know. Probably not. You'd be building a series capacitor of pretty undefined impedance with a cut in an antenna trace, and you'll end up sending RF energy somewhere in your board you don't want to. If it works with the external antenna plugged in, and you don't want to replace the device, leave it alone.