The only "things" that can't be purchased with XP by a Droid, ever, are Force Powers. They are the only things that have "Require Force Rating: X" as a rule.

Even Force Talents don't have that, Force Talents just require a Force Rating to be USED.

Pg. 275 of the Edge of the Empire core:

Players should be aware of additional limitations to becoming Force sensitive as well. For example, the Droid species cannot become Force sensitive, and certain other species open to player characters have similar limitations (this is listed in a species’ specific entry). Because these species cannot become Force sensitive, they cannot select the Force Sensitive Exile specialization.

I thought it was pretty explicit, but you can run Droids however you want in your game. Maybe you pumped some midichlorians into the oil and now have Force Sensitive Droids.

And yes, I just read the rule that says people without Force sensitivity can purchase force talents and not use them, so that would imply you don't need to be force sensitive to purchase a spec tree with force talents. As long as you aren't a droid, perhaps, unless you think the original entry was specific only to the Universal specs that provide Force Rating 1.

Something else that might be relevant, check out page 278 of the Force and Destiny rules "Lightsabers and the Force."

In case your Droid pc thinks he can build a lightsaber or take ranks in the skill (without some GM fiat).

Droids can not have a Force Rating. At all without some GM fiat. Which makes purchasing a Force unispec or starting in a Force career less than optimal. They can purchase Force specs after the fact though but will be unable to use any Force talents purchased. And I don't think anyone is stating that a droid should build his lighsaber(s). Grievous used lightsabers of those he had defeated. Nothing stops a droid from picking one up if he can and learning its skill if appropriate. a droid would be restricted to talents like parry so would never be able to reflect, but could still be a viable option.

Droids can not have a Force Rating. At all without some GM fiat. Which makes purchasing a Force unispec or starting in a Force career less than optimal. They can purchase Force specs after the fact though but will be unable to use any Force talents purchased. And I don't think anyone is stating that a droid should build his lighsaber(s). Grievous used lightsabers of those he had defeated. Nothing stops a droid from picking one up if he can and learning its skill if appropriate. a droid would be restricted to talents like parry so would never be able to reflect, but could still be a viable option.

Yeah, nothing should stop a Droid, or really anyone, from using a lightsaber, or even building one; the Force makes them more practical, but the skill doesn't require Force Rating 1+, so they're CAPABLE. Grievous does cheat by having "supernatural powers", in the form of he's a Cyborg, and has preternatural strength, agility, dexterity, flexibility, and possibly even sensors on other parts of his chassis, to gain "spatial awareness". He certainly can parry, and almost make shields out of his lightsabers, with his rotating wrists. Before the EU torch, various rich families purchased training droids for their Jedi-aspirants, even though the Masters weren't too keen on it. I won't do my typical "I hate that lightsabers seem to NEED the Force, now" speech, because I have, and no one wants to hear it, again (things change, and I whine ), but there are a number of things you can do with a saber, Force, or not. Building a lightsaber should also fall into this; you read a schematic, and follow the instructions, same as a blaster.

It depends how much of the rule book you consider to be rules:

There is one other arena in which Force sensitivity bestows a power not available to most individuals: the ability to wield the lightsaber...

Only those capable of supernaturally fine physical control can wield a lightsaber’s massless blade without great risk to themselves.

- FaD CRB

There's nothing supernatuaral about robots, but I can understand they can be programmed to wield just about anything. And although the hilt of a lightsaber is a relatively simple piece of tech in Star Wars, aligning the delicate parts to make use of the crystal and create the weapon is implied to require guidance from the Force.

Traitor, aka FN-2187, lost a fight to a guy wielding a cattle prod.

Was it really created to counter Lightsabers? As a weapon it would be useless against an actual Jedi with 1 rank in Force Move. 50 Blaster Rifle carbines firing simultaneously worked just fine during the Clone Wars. Why mess with success?