While the answer from @quartzic is a perfectly acceptable, I'd like to present an alternative.
The missing styles is most likely caused by Tailwind purging all styles that it doesn't detect being used anywhere in your code. This purge functionality can be configured by defining a safelist - a list of classes that shouldn't be purged under any circumstances.
In your case, I'd add the background color classes you want to use, to the safelist and you wont have to change anything in your React component. This is done in the tailwind.config.js
file:
module.exports = {
// ...
safelist: [
'bg-red-500',
'bg-blue-500',
'bg-green-500',
'bg-yellow-500',
'bg-cyan-500',
]
// ...
}
The downside is that it might increase your style bundle size, if your safelist includes classes that turned out to not be used anyways. In you case, this doesn't seem to be an issue though.
This safelist can even use regular expressions (although, I'd be vary of using that, as it might increase bundle size unexpectedly).
You can read more in the Tailwind documentation