Ok now that I have the project open – that background object will work correctly with transparency. But none of the display tags I see have their visibility turned on. (and more than Jim was alluding to – they don’t even have transparency set ) that might be a versioning thing – what version of C4D are you running?
FYI the visibility setting doesn’t really do a good transparency – its a more a faded density look. Using transparency in the material would give you more options with edges building up to show volume and rear faces more dense than close faces etc.
Do you have a reference image of the look you are going for? The display tag is more often used to make things not show up in the render and for matte generation than for making something transparent in the usual sense of the word.