Material UI has a colorManipulator utility file, which includes an alpha function:

import { alpha } from '@material-ui/core/styles/colorManipulator';

/**
 * Sets the absolute transparency of a color.
 * Any existing alpha values are overwritten.
 * @param {string} color - CSS color, i.e. one of: #nnn, #nnnnnn, rgb(), rgba(), hsl(), hsla(), color()
 * @param {number} value - value to set the alpha channel to in the range 0 - 1
 * @returns {string} A CSS color string. Hex input values are returned as rgb
 */

{
    backgroundColor: alpha(theme.colors.red, 0.5)
}

Alternatively, you can add the color library from npm for color manipulation:

import Color from 'color';

{
    backgroundColor: Color(theme.colors.red).alpha(0.5).string()
}

Alternatively, you can use the fade function provided in Material UI Next.

import {fade} from 'material-ui/styles/colorManipulator';

const theme = createMuiTheme({
  overrides: {
    MuiButton: {
      root: {
        boxShadow: `0 4px 8px 0 ${fade(defaultTheme.palette.primary[500], 0.18)}`,
      }
    },
  }
});

export default theme;

Here's how it's working : https://github.com/mui-org/material-ui/blob/v1-beta/src/styles/colorManipulator.js#L157-L164

Another solution could be to use similar color functions from https://github.com/styled-components/polished

Assuming you don't already have the alpha channel defined in the color, you can also do:

backgroundColor: theme.colors.red + '00' 

This will set alpha channel to 0, thus transparent. You can append any value between '00' to 'ff'