There is a huge gulf between the abundance necessary for criticality and that necessary for prompt criticality. Even rudimentary, low-yield weapons design requires HEU, likely over 50% 235 (and if you have the capability to enrich beyond 20%, the barrier to enriching up towards "weapons grade" is comparatively low.) I won't contradict the FAS's claim that this is within the reach of any _rogue state_, but it's not something you can achieve by bombarding natural ore with your garage-project fusor.
What stops you from using criticality in a breeder setup? Once you can produce enough plutonium, you have yourself most of the ingredients for a basic gun type weapon.
In any case, you have everything you need for a dirty bomb.
Usually "breeder" indicates a reactor with a fully closed fuel cycle that generates more fissile fuel than it consumes. A Pu-239 breeder would need to begin with critical mass of Pu-239 to begin this fuel cycle, in addition to the U-238 feedstock you are wanting to bombard. Kind of puts the cart before the horse. Additionally, the engineering for a liquid sodium or molten salt cooling system (water is too strong a fast-neutron moderator for this application) goes beyond the means of the hobbyist or extremist group.
I don't think this is what you meant, though. Why can't [an independent actor] recover Pu-239 from the core of a uranium reactor? I'll admit I don't know a lot about chemical reprocessing, but the proposition here is using a series of highly corrosive and/or explosive chemicals ([fuming] nitric acid, tributyl phosphate, hydrazine) to extract Pu-239 from very radioactive irradiated fuel rods with unknown actinide concentrations. Chemical reagents for this process (e.g. for PUREX, tributyl phosphate) are controlled and monitored by non-proliferation agencies. Chemical re-processing will not separate the Pu-240 from the Pu-239. Pu-239 is unsuitable for a gun-type weapon, as it is so fissile that it will blow itself apart in a partial detonation ("fizzle") before the slug and target are brought together--this means you need an implosion-type ("Fat man") weapon to effectively use Pu-239 as a fuel. A high concentration of Pu-240 exacerbates this problem. A fizzle in a populated area is still very bad, but not bad in a way that couldn't feasibly be produced by conventional explosives and/or chemical weapons much more easily. In order to produce enough Pu-239 to form a weapons core within years instead of decades or centuries (provided extraction is feasible), the independent actor probably is looking at a >1 MW reactor with the cooling towers and infrastructure that surrounds a project of that scale.
It is really only a viable threat for a terrorist organization if that organization has the clandestine support of a nation state.
EDIT: Or otherwise enough financial support, technical expertise, and freedom of activity to engage in serious construction projects and industrial chemistry. The point is that it's not something you can put together in a basement lab.