Some of the English Renaissance dudes were really Catholic, but posed as Anglican as a cover. It’s fine. We’ll take it.
They weren't shy about it either, but the royals knew better than to mess with them. They just looked the other way.
I don't know about Morley or about my new find -- Thomas Weelkes. We sang his "Alleluia - I Heard A Voice" recently, and it's like skyrockets going off all over the place. You can hear a snippet of it here.