Embeddable JavaScript widget with React
For the requirements you mentioned, the best solution is browserify (or similar). Using reactify transform you can have the JSX to JS happen all in one step. Browserify (and Webpack) are very common the react community, so nearly all libraries are published to npm for easy consumption.
Browserify packs your JavaScript, your React version of choice, and any libraries into a single JS file which doesn't use globals or other patterns that conflict with other code running on the page.
You can also look into some libs like react-css to isolate your styles from the page styles. The styles will also be isolated in your bundle. Of course if the page does something like div {margin: 1em}, the only solutions are iframes or web-components.