I am leaving this here just in case anyone else comes across this bug:
I looked into the code for both the plugins. I have created a ticket at wp-rss-aggregator plugin support page : https://www.ads-software.com/support/topic/incompatible-with-tablepress-export/
The problem is in admin-import-export.php,
if ( isset( $_POST['export'] ) && check_admin_referer( 'wprss-settings-export' ) ) {
For now, a quickfix would be to remove && check_admin_referer( 'wprss-settings-export' )and replace it with current_user_can capability check.
