Not Able to Access Terms Under Custom Taxonomy Archive

A 404 is the expected behaviour.

You’ll find no link to such a URL in the WordPress admin, there’s no functions to generate that URL in code, and there is no possible template for such an archive, as shown in the Template Hierarchy documentation (archive-movie-genres.php is not a valid template). The path /movie-genres alone will not return anything in WordPress under normal circumstances.

All WordPress templates are based around The Loop, and that loop is for looping over and displaying posts, not terms.