Modify function to only return values for the user that’s logged in

See below for my version of what you are trying to do. However keep in mind that adding this function to your functions.php, and changing the plugin to point to this function, will produce an error that the function does not exist. This is because plugins are included before functions.php, so when the plugin loads your function doesn’t exist yet. You will need to make this change inside the plugin itself.

Modifying plugins is generally not a great idea because as the plugin updates it will overwrite your changes. If you think that it is still a good idea in your case, I would suggest changing the name of the plugin, or setting the version number very high to prevent updates from breaking your code. Of course from then on it will be up to you to manually update/maintain the custom version of the plugin as needed.

function community_events_venue_select_menu_current_user( $event_id = null ) {

    global $current_user, $post;
    get_currentuserinfo();

    if ( $post->post_author != $current_user->ID ) {
        return; // Do nothing if this post author does not match our current user id
    }

    if ( ! $event_id ) {
        if ( isset( $post->post_type ) && $post->post_type == 'tribe_events' ) {
            $event_id = $post->ID;
        } elseif ( isset( $post->post_type ) && $post->post_type == 'tribe_venue' ) {
            return;
        }
    }
    do_action( 'tribe_venue_table_top', $event_id );
}
add_action( 'tribe_events_community_form', 'community_events_venue_select_menu_current_user' );