Content editor webpart overrides Sharepoint CSS

 CSS, Selectors and its rules for CSS Specificity and you will be able to master any CSS problem.

In your scenario you can wrap your content in a DIV unique  selectors ID

<div id='myCEWP'>
  <H1>Hello World!</H1>
</div>
And then apply your CSS only to that one H1 in the DIV :

<style>
   #myCEWP > H1 {
     color:green;
   }
</style>