Media Dialog CSS broken in WP v.5.3.2

My plugin displays the media picker dialog on the users front end. If a user has WordPress 5.2.2 installed then the media picker dialog looks nice/normal (see the first image). If they have WordPress 5.3.2 installed then the dialog seems to be affected by the front-end (theme?) styling.

Does anyone know how I can overcome this? Is this a known problem that WordPress knows about and is fixing?

Edit Actually, it seems to be looking normal on my v5.2.2 website due to other plugins being installed. If I deactivate them then I get the same styling issue.

I enqueue the media stuff in the 'wp_enqueue_scripts' action. Is that the problem?