I've either gone with Sass (via webpack/require) per component, or with JSS (my preference lately)... react-jss works pretty well, and I can always start with inline, change to jss as I go. Some things are a bit awkward starting out, but it's easier to share configs and common settings with JSS. My only complaint is the library is a little heavy.
Yeah, I was really interested in Aphrodite, but react-jss just seems slightly better in terms of a solution. It renders to style tag(s), so you can do media queries, and you can invert nesting similar to sass/less, so it's not bad.. remembering to quote css properties is the only hard part (similar to inline)... you get classes to set on your rendered components, similar to aphrodite (iirc), and it goes well enough.