You can simulate it with some significant markup and CSS pre-processing, but it's tricky. Polymer does this with it's templates.
BTW, CSS modules essentially automate and enforce BEM. Each component's CSS file can have a ".button" class that doesn't conflict with any other ".button" on the page because they're automatically name-mangled (https://en.wikipedia.org/wiki/Name_mangling). Then in your React code you do something like
import styles from "./supermenu.css"
SuperMenu = ({}) =>
<div className={styles.supermenu}>
<button className={styles.button}>Foo</button>
</div>
Or use something like react-css-modules to make it a little less verbose: https://github.com/gajus/react-css-modulesI'm not totally sold on this approach though. You lose some of the benefits of CSS, like theming.
But it depends on the CSS. A global button class will not overwrite the properties of a button class descending from a higher level class. It will only introduce new properties that are not already defined in the button that's inside the parent scope.
There are advantages to having base styles in a global class, but I agree they can get unwieldy if one doesn't have discipline with them.