For the Vatican city (and other Italian places of worship), would a slightly see-through kimono - like the attached picture - be allowed, or would they not allow it as you can sort of see the shoulders?
The places in Vatican that do have the dress code are St Peter Cathedral and Vatican Museum. Their official rules state that:
Low cut or sleeveless clothing, shorts, miniskirts and hats are not allowed.
From my experience even those rules aren't strictly enforced, and you'd see fair amount of visitors in shorts inside. I was there twice, both time wearing shorts. The photo above should be okay.
Other churches in Rome, however, seem to be more strict; generally the less touristy the church, the stricter it seem to be. I was denied admission to 2 out of 7 churches for wearing shorts, but none of them were in Vatican or in tourist spots.
And for the sake of clarity, the Vatican City itself does not enforce the above "dress code", as long as you're on the streets you can wear shorts and tank tops.