I cannot really make out a question in the body of OP's post, so I assume all of that is just meant as context of what this question (in the title) is about. I also am not familiar with the ramblings of the Unabomber and will ignore that aspect. So:

Is it true that a technological society has to weaken family ties and local communities if it is to function efficiently?

Yes, even disregarding any revolutionary terrorist pamphlets, there seem to be good objective reasons why technological advancement (before the information age) is correlated with weakened families and local communities.

At least between, say, industrialization and before the "age of information" this surely has some base in reality. In pre-technological days, i.e. hunter/gatherer tribes of a size where everybody could still personally know everybody else and very strong intra-tribal bonds, it can be assumed that most roles of members of the tribe can in principle be done by anybody. I.e., anybody can find some utility either as hunter or gatherer or someone who cares for others, and so on and forth. Surely there is specialization, but not so much that a person has to actually move to a different tribe - in principle everybody could, and probably did, live very close to their family for their whole lives. Migration between tribes certainly happened too, and it probably helped the tribes by moving information around and freshening up the gene pool, and hence making things more efficient, but I would assume this was a relatively minor role; sticking with the tribe was probably always much much easier for all involved.

In a technological era (after the advent of industrialization; before a high-end information age) there will be much, much higher specialization. Both within the dimensions of ability, as well as interest, which are arguably strongly interlinked via the observation that students who are interested in what they are studying have a much easier time with it, there is a much more intense stratification. And before the information age (i.e., at a time when people needed to actually physically move to where the work was), this moving-around surely lead to weakening family ties and local communities. If you move to another city, you are not in your family anymore; and if you don't have the internet yet, you can at best write snail mail or phone home regularly. This would often fall to the side, when the job got more intense. Also, when you move to a city, all local communities are foreign to you; and not every human has an easy time (or interest in) integrating into those.

Now, in the information age, especially since COVID, we see that it is very possible for information workers to stay at home. There are problems associated with that as well (isolation, depression and so on), some of them very dire (especially for kids who were isolated in their formative years), but not related to the aspects this question is about. Anecdotally, I see plenty of young adults who stay at home with their family much longer than it used to be - either because moving out is considered a waste of money or time, or because it's arguably often more convenient to stay home. One could hence imagine that a hypothetical society where all jobs are basically information based, i.e. possible to be done remotely, could revert back to much stronger family ties and local communities. (Disregarding for the sake of this question the problem that kids who were isolated seem to be having a hard time entering even local communities like they did before COVID...).

I cannot really make out a question in the body of OP's post, so I assume all of that is just meant as context of what this question (in the title) is about. I also am not familiar with the ramblings of the Unabomber and will ignore that aspect. So:

Is it true that a technological society has to weaken family ties and local communities if it is to function efficiently?

Yes, even disregarding any revolutionary terrorist pamphlets, there seem to be good objective reasons why technological advancement (before the information age) is correlated with weakened families and local communities.

At least between, say, industrialization and before the "age of information" this surely has some base in reality. In pre-technological days, i.e. hunter/gatherer tribes of a size where everybody could still personally know everybody else and very strong intra-tribal bonds, it can be assumed that most roles of members of the tribe can in principle be done by anybody. I.e., anybody can find some utility either as hunter or gatherer or someone who cares for others, and so on and forth. Surely there is specialization, but not so much that a person has to actually move to a different tribe - in principle everybody could, and probably did, live very close to their family for their whole lives. Migration between tribes certainly happened too, and it probably helped the tribes by moving information around and freshening up the gene pool, and hence making things more efficient, but I would assume this was a relatively minor role; sticking with the tribe was probably always much much easier for all involved. (All of this is admittedly very much speculative and very hard to tell in hindsight; a commentor mentions inter-tribe marriage to keep the peace.)

In a technological era (after the advent of industrialization; before a high-end information age) there will be much, much higher specialization. Both within the dimensions of ability, as well as interest, which are arguably strongly interlinked via the observation that students who are interested in what they are studying have a much easier time with it, there is a much more intense stratification. And before the information age (i.e., at a time when people needed to actually physically move to where the work was), this moving-around surely lead to weakening family ties and local communities. If you move to another city, you are not in your family anymore; and if you don't have the internet yet, you can at best write snail mail or phone home regularly. This would often fall to the side, when the job got more intense. Also, when you move to a city, all local communities are foreign to you; and not every human has an easy time (or interest in) integrating into those.

Now, in the information age, especially since COVID, we see that it is very possible for information workers to stay at home. There are problems associated with that as well (isolation, depression and so on), some of them very dire (especially for kids who were isolated in their formative years), but not related to the aspects this question is about. Anecdotally, I see plenty of young adults who stay at home with their family much longer than it used to be - either because moving out is considered a waste of money or time, or because it's arguably often more convenient to stay home. One could hence imagine that a hypothetical society where all jobs are basically information based, i.e. possible to be done remotely, could revert back to much stronger family ties and local communities. (Disregarding for the sake of this question the problem that kids who were isolated seem to be having a hard time entering even local communities like they did before COVID...).