My question is how can they have the above technologies with only mid-1980s-level computers? Is this even remotely possible?

We don't have any of those technologies with early-2020s-level computers, which means that they are either:

1. impossible to do with 1980s technology too, or
2. aren't dependent the level of compute power.

Your first three requirements require pharmaceutical and genetic engineering breakthroughs... of the three, I feel that it is the creation of novel hybrid species which seems like the least plausible thing. Lucky advances in artificial tissue growth and some novel handwavium approaches to antirejection drugs might explain commercially viable lab-grown tissues and organs. I don't actually know what the obstacles are to exowombs (and researching them is too much effort right now) so I'll pass on that one.

Of the latter two, LFTRs seem like they're just a Simple Matter of Engineering, and so handwaving them in seems just fine. It isn't immediately obviously that nuclear lightbulbs are possible at all... certainly, lots of research went into them, and some non-trivial amount of it remains classified, but they are crazy gonzo engineering ideas that seem somehow less plausible than magical hybrid species. I suspect there are better nuclear heavy lift designs you can build on which are less technically difficult, but that's a topic for another question.

My question is how can they have the above technologies with only mid-1980s-level computers? Is this even remotely possible?

We don't have any of those technologies with early-2020s-level computers, which means that they are either:

1. impossible to do with 1980s technology too, or
2. aren't dependent the level of compute power.

Your first three requirements require pharmaceutical and genetic engineering breakthroughs... of the three, I feel that it is the creation of novel hybrid species which seems like the least plausible thing, because it isn't obviously possible in the first place. Lucky advances in artificial tissue growth and some novel handwavium approaches to antirejection drugs might explain commercially viable lab-grown tissues and organs. I don't actually know what the obstacles are to exowombs (and researching them is too much effort right now) so I'll pass on that one.

Genetic engineering is the most obvious thing that will suffer from lack of compute power... genomes are large, requiring reasonable amounts of fast random-access storage, and assembling them requires a certain amount of computer time that may not be available in your setting.

Of the latter two, LFTRs seem like they're just a Simple Matter of Engineering, and so handwaving them in seems just fine. It isn't immediately obviously that nuclear lightbulbs are possible at all... certainly, lots of research went into them, and some non-trivial amount of it remains classified, but they are crazy gonzo engineering ideas that seem somehow less plausible than magical hybrid species. I suspect there are better nuclear heavy lift designs you can build on which are less technically difficult, but that's a topic for another question. It may be that you can build a closed-cycle gas core nuclear rocket without the aid of modern computer simulation and modelling tools, but honestly it seems pretty dubious to me.