Change SVG style properties from parent

Question

I have a component that references an external SVG file:

<div className='logo-wrapper'>
  <object 
    type="image/svg+xml" 
    className='logo' 
    data="/images/logo.svg" 
  >
  </object>
</div>

Inside the SVG file, I have declared styles:

<style>
  .cls-1{
    fill: red;
  }
</style>

I need to be able to edit the styles from the parent component, say, change .cls-1 to a green fill instead of red.

I have attempted to add classes to the parent component, however these don't seem to talk.

How does one do this?