Have you tried using layout containers? When you have multiple worksheets in the same layout container, the worksheets can collapse and vanish when they are filtered out.
PS: I also like the design of what you posted!
It's mostly possible. Using the bars across the top to choose your data is only possible if data is properly shaped to enable a worksheet and action filters. The method I posted in the attached uses a parameter, which doesn't have the same formatting options.
Each group of appearing/disappearing worksheets has its own Horizontal Layout Container, so in this case there are two layout containers. The Choose Dimension parameter is used as the value of a Chosen Dimension calculated field that is on the Filters shelf for each worksheet.
The color legend is actually a separate worksheet using the Square mark type so it will come and go and change values as the chosen dimension changes. This is because the standard color legend will be wiped out as the views change, but the legend title will still show up.
Worksheets must have at least one discrete (blue) pill on the Rows or Columns shelves, or else the chart will not be completely erased as the parameter changes.
In addition, the worksheets must not have their titles displayed - having the title in place will prevent Tableau from hiding the worksheet. If you need a title, either use fields to create headers in the worksheet or create additional worksheets.
A couple of extra notes on this method:
When worksheets are hidden, they don't totally disappear - each hidden worksheet takes about 20 pixels of space, you can see this as some whitespace on the left of the view.
If you manually fix a worksheet's width or height, then the worksheet will still take up that space even when hidden.
One more note: In the graphics you posted, you were using dashed lines for the projections. Tableau can generate vertical or horizontal reference lines that use dashes, but that is not an available option for the Line Mark Type.
It is awesome. this is what I need.