Reincarnation starts to make sense as we realize the truth of consciousness as something not confined by or dependent on our bodies. It's not a soul to soul transference according to the traditions who teach it because their is no individual separate soul in their view.
The heart is up to 5,000 times more magnetically charged than the brain, 60x more electrically charged, and the last place consciousness moves through when we die. The traditions that actually teach and realize the truth of the power of the heart experientially and not simply intellectually are worth looking into if we can do so with curiosity. But that's far off for most, we don't even think enlightenment is possible. Again, we entertain it intellectually, but hardly anyone believes that the Buddha or anyone was or is actually enlightened when it comes down to it. Start talking about the accomplished yogis and boddhisattvas who predict with creepy accuracy the place, time and conditions of their next birth and you lose everyone who approaches life mainly through thinking faculties.
I will say I unequivocally believe in the law of karma and ultimately that is what reincarnation points to, which is an applicable teaching to our life currently as it applies to our grasping mind and hangups.
In the same way we don't believe in reincarnation or enlightenment past the white-washed history of Renaissance concepts, many Tibetans and native populations don't believe we actually went to the moon. Basically we know what we know and I wouldn't be so quick to dismiss traditions/people who have spent centuries in contemplation and have actually broken the chain of karma and discursive thought. In my experience as someone who was completely dismissive of anything related with religion or occult traditions until I began practicing Buddhism all I can do is laugh when I realize the truth of something I've come across in myself.