The fluoride cooling salt used by Moltex does not use lithium or beryllium. Instead, it's sodium-zirconium fluoride or sodium-potassium-zirconium fluoride, with no isotope separation required. The atomic mass of these isotopes is high enough that the neutron spectrum remains hard. In fact, Moltex's design adds a bit of hafnium (a strong thermal neutron absorber that is chemically very similar to zirconium) to the coolant salt to shield the walls of the reactor from thermal neutrons.
One issue with fluoride salts in homogenous reactors is that the salt must be kept a bit oxidized, so uranium does not disproportionate into UF3 and U metal. The metal would plate out on surfaces, which is a no-no. Unfortunately, this means the salt must be oxidizing enough that it will dissolve chromium, so ordinary stainless steels cannot be used.
By using a barren coolant salt, Moltex can make the salt reducing enough that chromium is stable (they do this by using a sacrificial anode of zirconium metal.) Their design can use stainless steels that have already been tested and proven for use with the neutron exposures of fast reactors.
The chloride fuel salt in Moltex (and Terrapower) don't have that chemistry issue; uranium is more chemically stable there.
For thermal reactors, particularly if you want to breed, then you have to be very careful wrt losing neutrons (since you're barely with your nose above water to begin with), so there parasitic neutron capture becomes a very important parameter. And yes, in that regime FLiBe turns out to be a pretty good choice.
For fast reactors, you have more excess neutrons so you have a bit more freedom. Cl, being heavier, allows a slightly harder spectrum, which is good, though not that critical. That being said, there are many fast spectrum paper reactors using flouride salts as well (not FLiBe, but FLiNaK, or some ZrF salts etc.).
Would you mind expanding on this? Why?