Browsers have put years of efforts into making their CSS stylesheet parsing + rendering engines blazing fast and memory efficient. Inline styles haven't exactly had that same treatment. However the bright side is that it actually doesn't matter much if you're creating normal-sized apps/pages. The difference is miniscule. Inline styles make up for the fact that 100% of the styles are actually used, where CSS stylesheets are often concatenated and almost 90% of the parsed rules are inactive (wasted).
Tip: Improve your performance by avoiding React re-renders. That's where the bottleneck often really is!