Everything is generated through a config file which you can completely customise. So you could literally change the colour of bg-white if you wanted to.

It's part of the selling point, that config file becomes your design system. They provide a decent one but you are free to overhaul it as you see fit. It works really well.

If you were building a themeable website, then you'd not be using bg:white; instead you'd use something like bg:main or something similar with a semantic meaning. This kind of customization is one of Tailwind's core workflow.

This is a trivial, supported use case with Tailwind.

Read the docs for a few minutes and try it out, you may come to different conclusions than your current assumptions.