Is there a way to auto-sort your inventory, such as by item type or "Can [current character] equip this?"

Also, can the list of people you have reputation with be sorted by how much rep you have with each faction?

I wish!

The main issue is that there is too much loot and most of it is so similar that you can't even tell whether it's better than something you already have.
On my last mission I had to drop a lot of loot because I had no more space in the inventory, and that was all equipment, not coffee!

There is a single sort criterion, in the Loadout screen, between the progress indicator for the character's experience and the digital readout for your credit balance, just above the inventory.

The dialog will classify a list of items by their Type, Rarity, Value or using a custom filter based on Loot, Consumables, Weapons, Armor, Shields, Accessories, Character, and All (of these categories).

edit: punctuation & layout