The trick is to understand the strengths and weaknesses of any given framework and match those with the constraints of your project.
Things like jQuery and Underscore on down to stdio.h are libraries. You can pick and choose from what they contain but they're not so tightly coupled that they get in your way.
They're a tool belt with tools that do one thing and do it really well. Frameworks are like having a tool belt with a hammer that also has a saw on the end but in order to use the saw you have to grab the screwdriver even if you're not actually using it.
That said, React is a "A Javascript Library for Building User Interfaces." And to me me it does feel more like a library than a framework.
It takes your data as an input and by some mechanism lays out a visual representation of it defined by your components render methods, being sure to update the visual representation as the data changes. The rest are implementation details.