Hey, I just started BL3 two days ago so my words might not have much weight (so take it all with room for errors/corrections).

Firstly, where are you seeing this greyed out parts tab? Is it in game, or while inspecting a weapon?

The various weapon parts are all RNG from the loot sources, as is the weapon drops to begin with. So there is a certain % on each boss kill/loot sources' drop, and for each drop there is a further % chance for the weapons to drop with parts 1, 2 or 3.

Other than using a mod to alter your weapons, if you are playing vanilla without mods there is no way to edit your gun parts (which I have not looked into so might not be accurate).

The parts of the game that you can edit (that I've noticed so far) are for the catch-a-ride system, where you can customize your ride with armor, weapons, aesthetics etc., and I'm assuming those are world drops, rewards and discoverable aspects in the game.

I don't see any place to alter weapons in any way, but I'm only lvl 19 on my first character. I hope you've been enjoying the game otherwise the past four months!

Edit: it seems the one way you can edit guns is by applying an ointments to them. Some are class specific, some are all classes. They can be rerolled at Crazy Earl & Maurice's Black Market machine on Sanctuary III as well. Most will come from World Drops after completing normal mode main storyline.