score:3

Accepted answer

You can do this is CSS by adding the following class and style rule.

!important is needed to override the react-bootstrap library's style.

.Btn-Blue-BG.active {
  background-color: blue !important;
}

and

<ToggleButton className="Btn-Blue-BG" ...>

See demonstration below:

https://codesandbox.io/s/6nwkwnn29z

score:1

Did you try adding bsStyle="primary" ?

<ButtonToolbar>
    <ToggleButtonGroup
        type="radio"
        name="options"
        value={...}
        onChange={...}>
        <ToggleButton ... />
        <ToggleButton bsStyle="primary" />
        <ToggleButton ... />
        <ToggleButton bsStyle="primary" />
        <ToggleButton ... />
        <ToggleButton bsStyle="primary" />
        <ToggleButton ... />
      </ToggleButtonGroup>
    </ButtonToolbar>

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