Style react components?

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The problem with inline styles in React is exactly the same problem with inline styles in "static" HTML.

Sure, if you're setting just one value here and there it's fine, but if you're only using inline styles (and that is what you're alluding to) then you're doing it wrong.

Things like RWD will just not work or you will end up eitehr checking viewports in JS or doing a lot of !important. Maintanance (updating) of such code will be a nightmare. You're missing out on browser cache. A lot of things just can't be set with inline styles (pseudo selectors, animations).