Libraries like MDL work by waiting for the page to load using the DOMContentLoaded event, scanning the page for things like input elements and manipulating them with JavaScript so that they can inject the bits and pieces needed to work with their components. This works fine on static websites, but the DOMContentLoaded event only fires once, so when Angular performs a page transition, the DOM changes without MDL knowing about it.
Material Design Lite has a section in its FAQ about using MDL on dynamic websites:
Material Design Lite will automatically register and render all elements marked with MDL classes upon page load. However in the case where you are creating DOM elements dynamically you need to register new elements using the upgradeElement function. Here is how you can dynamically create the same raised button with ripples shown in the section above:
<div id="container"/>
<script>
var button = document.createElement('button');
var textNode = document.createTextNode('Click Me!');
button.appendChild(textNode);
button.className = 'mdl-button mdl-js-button mdl-js-ripple-effect';
componentHandler.upgradeElement(button);
document.getElementById('container').appendChild(button);
</script>
Of course, this probably isn't terribly easy to do in your case, since you'd have to manually find each new element and call upgradeElement on it.
Usually, instead of doing this sort of event-based DOM manipulation, Angular uses directives to initiate DOM changes. Consider using a library built to interoperate with Angular, instead, such as Angular Material.