Quick and dirty hack to make pure functions work in React:

pureFunctions.js

function component(fn){
  class C extends React.Component {
    render(){
      return fn(this.props, this.context)
    }
  }
  C.displayName = fn.displayName || fn.name
  C.propTypes = fn.propTypes
  C.contextTypes = fn.contextTypes
  return C
}

var pure = new WeakMap()

React.oldCreateElement = React.createElement

React.createElement = function(tag, props, ...children){
  var realTag = tag
  if(typeof tag === 'function' && !tag.render && !tag.prototype.render){
    if(!pure.has(tag))
      pure.set(tag, component(tag))
    
    realTag = pure.get(tag)
  }
  return React.oldCreateElement(realTag, props, ...children)
}

Your pure functions will have this simple signature:

(props, context) => ReactElement

Further, it supports displayName, propTypes and contextTypes:

function MyPureComponent(props, context){...}
MyPureComponent.displayName = 'MyPureComponent'
MyPureComponent.propTypes = {...}
MyPureComponent.contextTypes = {...}

It DOES NOT support state. That is a feature.