You mentioned injectFirst in your question, though your sandbox example wasn't using it. You should use it since this will make sure that the CSS from your CSS modules is inserted after the Material-UI CSS in the <head> element. When specificity is the same, the styles that occur later will win over earlier styles.
The default styles for the checkbox colors are as follows:
colorSecondary: {
'&$checked': {
color: theme.palette.secondary.main,
'&:hover': {
backgroundColor: fade(theme.palette.secondary.main, theme.palette.action.hoverOpacity),
// Reset on touch devices, it doesn't add specificity
'@media (hover: none)': {
backgroundColor: 'transparent',
},
},
},
'&$disabled': {
color: theme.palette.action.disabled,
},
},
Below is the corresponding CSS generated by JSS:
.MuiCheckbox-colorSecondary.Mui-checked {
color: #f50057;
}
.MuiCheckbox-colorSecondary.Mui-disabled {
color: rgba(0, 0, 0, 0.26);
}
.MuiCheckbox-colorSecondary.Mui-checked:hover {
background-color: rgba(245, 0, 87, 0.04);
}
@media (hover: none) {
.MuiCheckbox-colorSecondary.Mui-checked:hover {
background-color: transparent;
}
}
The important aspect to notice is that the checked style is done via two classes. In order to override these styles you need that same degree of specificity or greater.
Below is a full working example overriding the checked color of the checkbox:
index.js (important part here is <StylesProvider injectFirst>)
import React from "react";
import { render } from "react-dom";
import { StylesProvider } from "@material-ui/core/styles";
import CssModulesButton from "./CssModulesButton";
const App = () => (
<StylesProvider injectFirst>
<CssModulesButton />
</StylesProvider>
);
render(<App />, document.querySelector("#root"));
CssModulesButton.module.css
- Uses two classes in the style declaration -- the
checkboxtest CSS module class and Mui-checked (the global class which Material-UI adds for the checked state)
.checkboxtest:global(.Mui-checked) {
color: blue;
}
CssModulesButton.js
import React from "react";
import styles from "./CssModulesButton.module.css";
import Checkbox from "@material-ui/core/Checkbox";
export default function CssModulesButton() {
return (
<div>
<Checkbox className={styles.checkboxtest} />
</div>
);
}

Follow-up question from the comments:
Could you explain why can't I use classes? Shouldn't classes={{checked:styles.AnyClass}} overwrite the styles successfully? I understand why it doesn't, but what is the purpose of classes then?
You can use the classes prop, but there isn't any compelling reason to do so in this case. The following will also work, so long as the declaration for the styles is the same (using two CSS classes) so that you have the appropriate degree of specificity:
<Checkbox classes={{ checked: styles.checkboxtest }} />

As far as the second part of your question ("what is the purpose of classes then?"), there are two main reasons to use the classes prop. Some of the CSS classes for the classes prop get applied to different elements within the component, and some only get applied when the component is in a particular state, or when certain props have been used on the component. In this case, you are trying to target these styles for a particular state of the component. In v3 of Material-UI, you would have needed to use the classes prop to provide a class name that would only be applied for the checked state, but in v4 Material-UI switched to using global class names for these states (more details here: https://material-ui.com/customization/components/#pseudo-classes) such as Mui-checked. This makes it easier to target these states via a single generated class (a big driver of this change was to make it easier to customize Material-UI components using styled-components).