I've gotten closer, but not quite at a solution yet.

The main issue is that MUIButton injects a tag to the element to power the styles. This isn't happening in your unit test. I was able to get this to work by using the createMount that the material tests use.

After this fix, the style is correctly showing up. However, the computed style still doesn't work. It looks like others have run into issues with enzyme handling this correctly - so I'm not sure if it's possible.

To get to where I was, take your test snippet, copy this to the top, and then change your test code to:

const myMount = createMount({ strict: true });
  const wrapper = myMount(
    <MuiThemeProvider theme={theme}>
      <MyStyledButton variant="contained" color="primary">
        Primary
      </MyStyledButton>
    </MuiThemeProvider>
  );

class Mode extends React.Component {
  static propTypes = {
    /**
     * this is essentially children. However we can't use children because then
     * using `wrapper.setProps({ children })` would work differently if this component
     * would be the root.
     */
    __element: PropTypes.element.isRequired,
    __strict: PropTypes.bool.isRequired,
  };

  render() {
    // Excess props will come from e.g. enzyme setProps
    const { __element, __strict, ...other } = this.props;
    const Component = __strict ? React.StrictMode : React.Fragment;

    return <Component>{React.cloneElement(__element, other)}</Component>;
  }
}

// Generate an enhanced mount function.
function createMount(options = {}) {

  const attachTo = document.createElement('div');
  attachTo.className = 'app';
  attachTo.setAttribute('id', 'app');
  document.body.insertBefore(attachTo, document.body.firstChild);

  const mountWithContext = function mountWithContext(node, localOptions = {}) {
    const strict = true;
    const disableUnnmount = false;
    const localEnzymeOptions = {};
    const globalEnzymeOptions = {};

    if (!disableUnnmount) {
      ReactDOM.unmountComponentAtNode(attachTo);
    }

    // some tests require that no other components are in the tree
    // e.g. when doing .instance(), .state() etc.
    return mount(strict == null ? node : <Mode __element={node} __strict={Boolean(strict)} />, {
      attachTo,
      ...globalEnzymeOptions,
      ...localEnzymeOptions,
    });
  };

  mountWithContext.attachTo = attachTo;
  mountWithContext.cleanUp = () => {
    ReactDOM.unmountComponentAtNode(attachTo);
    attachTo.parentElement.removeChild(attachTo);
  };

  return mountWithContext;
}