Thorium people have not stopped their activity, but they suffer from financing issues.
If the question is - "what if history turned another way" - then Reagan could possibly be your point of divergence, as it was a political decision to shut down the process. It had probably bunch of aspects behind the scene, having plutonium sure one of them. Efficient burning was not the goal, but getting specific types of isotopes was.
So a high energy demand, successful breakthroughs in problems, the possibility to make Plutonium, some accidents with solid reactors at early stages like Chernobyl to build public resistance for those types of reactors (so it means actually some serious errors in process of developing nuclear reactors, to be too optimistic and go big too soon)
So significant negative pressure could limit solid reactors to military goals only. And military played significant role in developing those reactor for their purposes.
World's First NUCLEAR SALT REACTOR - Documentary Films pretty interesting history kind video. (they blame Reagan, saying that if he would be more familiar with technology he could decide other way)
Positive factors which could keep a molten salt reactor afloat could include space program like moon base, mars base.
Salt reactor, one of reason to start that program was wish of military to use it in aircraft, and conventional reactor was not capable to do that, but a molten salt reactor could in theory (even if the creator did not believe that it would work in a plane) to be used there.
For use in space, it has advantages too, one advantage being the more efficient use of fuel without expensive and technology intensive processes to recover fuel, to reassemble fuel rods. A lower reactor mass and simpler management are also very significant advantages for use in space.
It is also much easier to deliver the initial fuel - because of how it is packed. There is much less danger in the case of a mishap during launch, because of how it can be packed. It is easier to work with thorium as a main fuel source. There are also pretty significant amounts of it on the surface on the moon (12 ppm is about 70 tonnes per million tonnes of dust, thorium is ca 230 atomic mass, average for moon ca 30 atomic mass, so it is 12 * 7 tonnes per million, my rough estimation, even in the unlikely case that there are no concentrated ores)
According to fast link
- Thorium reactors deliver 3.6 billion kWh of heat per ton of thorium,
which implies that a 1 GW reactor requires about 6 tons of thorium per
year, assuming its generators are 40% efficient.
So it would be enough for a 10GW reactor, which will generate 315 GJ of electricity per tonne of ore. On the moon efficiency can be higher overnight, just as a note. Glass production uses 9GJ per tonne of product (mostly for melting), Aluminum production uses 54 GJ per tonne (because of the energy requirements of reduction of Al2O3 into Al). So you basically can melt it (ore) all down, reduce all stuff to pure metals and gases by electricity and it will be something like 20% of what you will produce after extracting the thorium. Not saying it is the way to do, but why not if you need Iron, Aluminum, and Titanium - which are present on the moon: some NASA thoughts about Al on the moon
So a strong lunar program could be one of the factors in favor of molten salt reactors.
One of the factors involved in solid reactors being preferred is investments from the military, they wanted them for a bunch of reasons.
Thorium reactors for a lunar base are an excellent choice, so they may have happened during the Appolo era, if there were other factors enabling moon base. This will aid progress in other areas, not just nuclear related problems, and could be one of the factors that could open perspectives for this technology to be more attractive, or enough attractive to pour money into it, and that is actually all it needed at that time.
So it may be not a big stretch, that history of molton salt reactors could be different.
P.S. as people have mentioned the Russians, so will I. Greater successes for their moon program could be also one of the factors supporting an expanded US moon program, without collapsing it. So moon base race could be an enabling factor too.
Note
read in case factual incorrectness feeling. disclaimerTM, do not build it at homeTM, make your own research before buildingTM, call me if u didTM
In this answer I rather project words of other, who are optimistic about thorium reactors and who thinks that problems can be solved.
Also it is not mention explicitly, answer keep in mind one particular type of possible types of Thorium reactors, molten salt with in situ utilization.
Packing benefits assumes packing fuel pellets, like in Pebble bed reactor, and relays on possible advantages dividing fuel in to small packages, encapsulating them in robust shell which can withstand fall from orbit if needed, where shell may be actually non radioactive part of future fuel(same thorium actually). It may be non radioactive (as Thorium non radioactive, not as completely non radioactive) in case of some kind of ADS(accelerator-driven system) as starter for whole process. There is difference with uranium rods, which I think can be exploited to our advantage.
Each reactor development includes lot of work behind the scene. This is complex work, which includes solving non obvious for the public or outsiders set of problems. If everything would be easy and simple, then it would be solved in the past, and we would not have question may or may not it to be solved. It wasn't, and question is valid.
Simplicity of main concept, does not mean that solution will be simple, it does not mean it is possible at all, at least at some technological level, which looks sufficient for solving that problem, but in fact, it is not sufficient and needs involving of more advanced technologies, to make it working or just working.
Some examples for better illustration:
Examples of such, which comes in my mind right now, as example knife. It is very old design, stone age old, but really good results where achieved after work with metal became more usual practice.
Another relatively simple idea as Space Elevator, with less obvious problem not exactly but like - to have easy access to space, u have lift huge amount of stuff or build that in space - both looks like easy access to space help here. Obscure/contrast it a bit more - to get easy access, u better have easy access. Even it almost technically possible to build such cable as just rope, u need more advanced rocket systems, or another and better launch technology it is possible, but would u need elevator then?
3He as fuel in thermonuclear reactor there are objections based on speed of reactions which would have place in such reactor.
Launch loop where main problem is reliability at current level of tech.
So there are interesting and promising things which looking good, but do not work at current tech level, for understandable reasons. How advanced we should be to solve them, who knows? Those who knows about thorium dividing in 2 categories believers and non believers, but none of them can prove that other side is wrong. One side not failed yet, but also do not have great success. Other side can point those 2 facts, but can't state it is not possible, exactly because of those 2 facts, but they try to make their reactors better, just in case(for reasons of waste). So this race is not ended yet.
Interesting links
play scientists, investigate isotopes chains - periodictable.com, isotopes, Th
Thorium optimists site energyfromthorium.com, they recommend this video 2h video "NASA" - Thorium remix 2016 to watch, I expect it to be at least interesting, but have not watched it yet.
Thorium fuel cycle, and specially "List of thorium-fuelled reactors"
Molten salt reactor concepts in general, https://en.wikipedia.org/wiki/Molten_salt_reactor