How to reproduce:

1. Open a new project
2. Create a script called "testGetType.cs" with the following code:

using UnityEngine;
using System;

public class RequestedClass {
//I'm a class!
}

public class testGetType : MonoBehaviour {

Type operatorType;
void Start () {
operatorType = Type.GetType("RequestedClass");
}

void OnGUI() {
GUILayout.Label ("Is the operator null? " + (operatorType == null));
GUILayout.Label ("What is the operator? " + operatorType);
}
}

3. Attach the script to any game object in the scene
4. Play the scene
- Note how the text shows that the operator type is not null, and that it is of the type RequestedClass.
5. Build to WebGL and run
- The text now shows that the operator type is null and does not return anything for the type.

A simple workaround would be to change the code at

operatorType = Type.GetType("RequestedClass");

to

operatorType = Assembly.Load("Assembly-CSharp").GetType("RequestedClass");