I think people take the word “reincarnation” for granted, and you can not blame them. Even Scott Alexander from SSC indulges in stress free Buddhism. Basically a way to purify ones mind into better understanding the true teaching of the Buddha. But who would you rather trust? Ancient “religion” who survived 2500 years and the communities still live. Or just a pragmatic guy who you need to pay 10$ a month for his meditation app. Spirituality is it thought in here, the commercial term. Sam harris’ no self ideas are core teaching of the Theravada along with monastic life and rigidness. But Theravada doesn't deserve its bad reputation, many countries that are Theravada monk at age 20 and they then quit are better off that self delusional “spiritual enlightenment” obsession that people have.
Cambodia and Sri Lanka are interesting countries because the core of their faith is Theravada but their politics is down right laughable. Cambodia there is no law FWIW. The only thing missing in countries eastern of us are Judeo-Christian values (Western society is build) Christianity should be more thought about how to treat other externally better. And Buddhism how to make sure your inner harmony can do that.
So from a rational point of view, what is reincarnation? There was a study about reincarnation Dr. Ian Stevenson but it has nothing to do with reincarnation proof but rather with scientific process problems. (He failed under confirmation bias, but this man has lived amazing experience, side note: he met with Huxley the author of brave new world). This can be like a reminder that reincarnation is just not possible (beyond cryonics and mind uploading) and telling that it can not be disproven is just missing the point.
Problems like this arise from happy death spiral of Buddhism. Zizek the philosopher criticised us for adapting such philosophies, calling them late stage capitalism of sorts.
A rational prediction would be: just like communism gradually disappeared in the 20th centuries. And capitalist thrived. Like that the Chinese civilization would become a better economical and superpower along with the philosophies of its origin (Western countries would indeed advance with this stress free commercialised buzzword). You just can not compete.