Reloading a crossbow requires a free hand, even as part of an attack action, unless the crossbow is self-reloading.
GM's who hogtie themselves to rules which are written in the context of common sense and verisimilitude but which 'gamers' use to force advantageous change in the game to 'max dps' or whatever are missing the point entirely.
Nowhere does it explicitly say the arrows to be used in a bow attack have to be readily accessible. As per RAW they could be tied up at the bottom of your rucksack, but they are there and the reload is as part of your attack, so you cross them off your character sheet and roll d20. You don't need a quiver either as per RAW - but we all know in a mobile fight you need this for firing more than a handful of shots because, you know, an IQ over 60 and COMMON SENSE...
If a player in my game fires two pistol crossbows in the first round that's fine, because they get a free object interaction for the holstering of a crossbow whilst the other is loaded. They cannot have both hands full all the time and reload as part of the attack every round, it cannot be done without a third arm, a spring loaded clip or a modified mage hand effect that follows them around.
Anyone who argues against basic common sense for 'rule of cool' reasons needs to read Wheaton's Law, and any GM who let's themselves be overriden by such munchkin rules lawyer tactics needs to re-read the bit in the rules about the GM being final arbiter. That's a rule too, and one which is paramount in such situations.
A GM should always have a reasonable point before ruling, but that said, it's their call.
Duel wielding hand crossbows with the feat is a prime example of this interplay, and the idea that someone can argue that the impossible is possible simply because the RAW doesn't disallow it (even though the moment anyone tried it in reality it would make their argument fall apart) is being a smart ass and needs to hear the word "no" from their GM.
By all means put in self-reloading hand crossbows in your game if you want flurries of fast fired bolts from dual wielders, but stop pretending that normal hand crossbows have this ability and that the rules cover every possible eventuality and simulation of reality and that you cannot use your brain or simple logic to rule on issues where nothing is explicitly stated in detail when you find that the rules don't in fact do so...