Selectively hiding or allowing thumbnails of featured images on front page

A custom field would certainly do the job. If you wanted a slightly more elegant way of doing it, you could make a meta box (or maybe even hook the featured image box…not sure if that’s doable or not off the top of my head) and add a checkbox for ‘Display on Frontpage’ or something like that.

Once you have that, its just a matter of modifying the loop on your frontpage so that (and this is pseudocode…so don’t think it’ll work)

if( custom_post_meta == desired_custom_post_meta ) {
     the_post_thumbnail();
}

and you should be done!