Since spaghettis were made by Italians and often set in Mexico or nearby there were a lot of catholic religious imagery and other such things in these films, this is part of the Latin culture. There were also moments of anti-clericalism though, in Django (1966) for example. But maybe this is another thing?
Alberto Cardone used quotes from the Bible in his Westerns Sette dollari sul rosso - The Spaghetti Western Database (spaghetti-western.net) and Mille dollari sul nero - The Spaghetti Western Database (spaghetti-western.net) as prologues or epilogues. The quotes related directly to the story being told and added some nice weight and depth to it. Gianni Garko’s Vigliacchi non pregano, I - The Spaghetti Western Database (spaghetti-western.net) also used a Bible quote in its prologue.
There’s normally not too much symbolism in regard to Catholic imagery in the SW genre, it was mainly historic accuracy that most Western towns did have some form of religious service in the community, though usually Protestant Christianity was practiced in those days, Catholic churches mainly being found in Arizona and towns that were at and near the Mexican border.
I can totally see guys like Sergio Corbucci wanting to take pokes at religion, and as we all know Lucio Fulci made those pokes every chance he could, Western or otherwise, but I’ve never felt like a lot of that was present in the majority of SW’s I’ve watched.
Maybe you should have juxtaposed the Miserere with another Morricone piece, as he has cheekily worked one of its musical phrases into the chorus of Vamos a matar, compañeros. 
Ah, didn’t know this, I’ll have to listen for this, thanks.
But yes, Morricone borrowed from both religious music and classical music.
The angelic choir and the soprano is what I think is similar in style in Miserere and L’estasi dell’Oro.
And of course both angelic choir and soprano voice is in other SW music as well.
There’s Catholic liturgy in ‘Return of Ringo’. In particular the ‘gringo’ funeral that’s intruded on by Don Francisco and Esteban Fuentes - with some comic effect from Fernando Sancho - “Ora pro nobis… Ora pro nobis…”
Kevin Grant devotes half a chapter (‘Relatives and Religion’) to this topic in his book ‘Any Gun Can Play’.
Interesting. 