How do I fix "Cannot assign to read only property 'style' of object" in this React component?

I am creating an own custom tab component. It consists of a tab header which each has a body part. When a tab header is clicked, the corresponding body's style should be set to display:block and all others to display:none.

For some reasons I am getting this error:

Cannot assign to read only property 'style' of object

I understand that I am not allowed to mutate the style property manually as it seems to be read-only but how do I fix/work around this?

Here is my code:

Tabs.js

import React, { Component } from 'react';

class Tabs extends Component {

  constructor() {
    super();
    this.state = {
      activeIndex: 0,
    };
    this.tabHeads = [];
  }

  // Initial composition of tab heads
  componentWillMount() {
    React.Children.map(this.props.children, (el, i) => {
      const tab = el;
      const key = `tabKey${i}`;
      this.tabHeads.push((
        <div role="button" onClick={e => this.onTabClick(e, i)} key={key}>{tab.props.title}</div>
      ));
    });
  }

  // Called when user clicks a tab head
  onTabClick(e, i) {
    this.setState({ activeIndex: i });
  }

  render() {
    // Set display none or block for each tab
    React.Children.map(this.props.children, (el, i) => {
      const tab = el;
      let visibility = 'none';
      if (i === this.state.activeIndex) visibility = 'block';
      const newStyle = Object.assign({}, tab.props.style, { display: visibility });
      tab.props.style = newStyle;
    });

    return (
      <div style={this.props.style}>
        {this.tabHeads}
        {this.props.children}
      </div>
    );
  }
}

export default Tabs;

Usage is like this:

render() {
  const tabStyles = [
    { padding: '20px' }, // Tab 0
    { padding: '20px' }, // Tab 1
  ];

  <Tabs>

    <Tab style={tabStyles[0]} title="Tab1">
      <div>Content 1</div>
    </Tab>

    <Tab style={tabStyles[1]} title="Tab2">
      <div>Content 2</div>
    </Tab>

  </Tabs>
}