I'm a pretty logical person and would never have believed in this kind of thing, except that I'm currently in a relationship with (and about to get married to) a man who is exactly like the "twin soul" described in the things you've been reading!
We've both had bad relationships in the past, and messy divorces, but this relationship is completely different. We've never argued. Never even raised our voices with each other, as we can discuss absolutely anything, rationally and respectfully.
But the "woo" part is that we've had virtually identical lives up to this point, despite being born 5 years apart and in different countries... We've both moved around quite a lot, but have lived in many of the same cities - just not at the same time. We studied the same subjet in the same city, but he graduated the year before I started. When we moved in together, we discovered we have identical record collections. Our teen years were also similar, we both married young and had our kids at exactly the same ages.
We have identical tastes in pretty much anything and almost always order the same dishes in restaurants, without consulting each other, or come home having bought the same thing for the house etc.
In fact, half the time, we don't even need to open our mouths to communicate, as we instinctively know what the other one's thinking. It really is like having a twin 