Unless you're doing Master/Expert end game recipes, crafting materia is mostly useless as long as you keep your crafting gear up to date. Sell it.
Unless you're doing a lot of timed node gathering, gathering materia is mostly useless as long as your gear is up to date. Sell it.
Unless you're doing current high end EX trials, Savage/Ultimate raids, combat materia is 100% useless (you don't get any benefit from it in level synced content). Sell it.
The only dyes worth keeping are the GP dyes you know you're going to use and aren't at rock bottom prices on the marketboard. Sell the rest.
Don't hoard fishing tackle that you aren't using on a weekly basis. Buy what you need when you need it. Discard or sell it when you're done.
Dump the fireworks/Magicked Prisms. You've probably never used most of them outside of testing one when you first got it. It doesn't hurt to keep a stack of Realm Reborn Red, Heavenscrackers and Meteor Showers but dump the rest that you aren't using frequently or never use. You can sell them cheap on the marketboard now to make inventory space then buy them back cheap in the future when you actually want to use them (which will probably never happen).
They've already told us they will not give us specialized inventory for things like dyes and tackle. When they're able to add more inventory space for players it will be general use that players can use as they like, same as when they added the chocobo saddlebag.
You're right that you're not the only one with a hoarding problem but you don't help hoarders by giving them more space. That just encourages them to keep hoarding. Take this as an opportunity to learn to control the compulsion to hoard.
Somewhat ironically, I disagree with this.
But it's not because of inventory space. It's because market listings are tied to retainers.
40 listing spaces is not enough for an active player, especially if they are into crafting/gathering. Unless SE is going to either greatly increase market listings per retainer or detach listings from retainers and go with a different market system, players will continue to get more retainers even if the inventory space is mostly/completely empty.