For expressing the religious concept of being "saved," what is the difference between salvo and salvado? Is there any difference in connotation or formality of the two words? Are there any contexts where one word would be correct and the other incorrect?
Basically the two terms mean the same thing.
That being said "salvo" is an adjective and "salvado" is the conjugation of the transitive verb "salvar" so the use of the words is slightly different:
As a native speaker I feel obligated to add that I have never heard the word "salvo" in a different context other than the religious one, which does not mean that it would be incorrect to use it only that it may not be that common.
I would say, that at least in Spain, the only one of them used in Religion is "salvado", as a participle of the verb "salvar".
If you look up the definition in RAE of "salvar" you'd see this:
which I think it's the exact definition you're looking for.
While for salvo the closest meaning is probably:
which is not the same. It's simply to be in a safe place or situation after being in danger.
In some resources through the Internet "salvo" is said to be an irregular participle of verb "salvar" (though the official resource RAE only gives "salvados"). If "salvo" can be a participle of salvar then both forms would be also acceptable. Maybe in the past it was used in that way but right now, at least in Spain, nobody says things like: