A vast majority of fashion items are obtainable through means of AP or items that allow you to obtain things that are easiest to get through means of AP (like Eden Crystals for the Crystal Altar, for example). But fashion items that are obtained through means of AP are tradeable, so you can also buy fashion items off of players who do actually buy and spend AP. But fashion items aren't cheap, especially prime fashion items, so it will cost you.
However, in regards to unstatted fashion items, you can actually get some through grinding repeatables. You should be getting Alpaca Coins (copper in particular) that, when you turn them in and get capsules, you'll get undyable, non-statted fashion items that you can wear and even archive. And when you hit 50, some non-statted fashion items even drop from trial bosses (very rarely) so there are other means of getting some until you've made enough money (or decide to spend AP on) prime fashion items with good stats.
On the bright side, with the new Arcane Box feature, non-statted fashion items can be combined to get better, statted fashion items (I'm not too sure if this counts for costumes received through Alpaca coins but I can only assume so) at percent chances, so there are more ways than just buying and spending AP.