Would it be possible to exclude certain roles from the plugin?

Thanks for the suggestion, but this is outside the scope of this plugin.

The Disable Embeds plugin completely removes any traces of the ability to embed other WordPress posts and make your own posts embeddable—for every user and user role.

Excluding certain roles from this would make this impossible and thus break that premise.

I’m sure there are other plugins out there that might do what you’re looking for.