Obviously this part is a mixed up one, and one has to consider it has to match with the music etc...but I can go further in my subtle analisys
-
padre nostro = our father. Mika said this part mocks the prayers he was obliged to say when a child, and this is the incipit of the most common one.
-
deus is latin anyway.
-
dio č madre = god is mother. When the pope mentioned that god is mother and not only father, he clearly did not want to assume that god is bisexual

but that god is capable of the same tenderness a woman is. Probably he also wanted to raise the feminine to a higher level....

Mika is using this statement for his own personal goal
-
machismo. This word is not Italian but is commonly used in Italy as well with its original meaning.
-
dio, sesso, santo spirito = god, sex, holy spirit. The holy spirit in the Catholic trinity is the entity which keeps Father (god) and Son (Christ) bonded in love and the one who got the Virgin pregnant. Matching it with sex is another Mika's clever sentence.
I don't know if all this is behind Mika's choice of words, but I think it's something more than a simple mix-up.