complicated hide/unhide rows on protected sheet

I added some formulas into your column Y yellow cells that will put an "X" in the rows that are to be hidden.
I added a BeforePrint macro into your ThisWorkbook module which will hide all the rows with text showing in column Y, print, then unhide.

Private Sub Workbook_BeforePrint(Cancel As Boolean)
    Application.EnableEvents = False
    Cancel = True
    With Sheets("Budget Sheet")
        .Range("Y:Y").SpecialCells(xlCellTypeFormulas, 2).EntireRow.Hidden = True
        .PrintOut
        .Range("Y:Y").SpecialCells(xlCellTypeFormulas, 2).EntireRow.Hidden = False
    End With
    Application.EnableEvents = True
End Sub

If you're satisfied with the results, you can hide column Y.