Remove react router

[chawes13]

Resolves #416

This has been on my todo list for a long time and felt like an appropriate inclusion with the modernization effort (especially given how old react-router@3 is).

Author Checklist

• [ ] Add unit test(s)
• [ ] Update version in package.json (see the versioning guidelines)
• [ ] Update documentation (if necessary)
• [ ] Add story to storybook (if necessary)
• [X] Assign dev reviewer