Ah, the problem was that you already had a filter area applied. I included to remove any filters before applying mine and that seems to have taken care of it:
    Dim rngDest As Range
    Dim rngCopy As Range
    
    Set rngDest = Cells(Rows.Count, "C").End(xlUp).Offset(1)
    
    With Intersect(ActiveSheet.UsedRange, Range("W51:W" & Rows.Count))
        .Parent.AutoFilterMode = False
        .AutoFilter
        .AutoFilter 1, "0ADD ID"
        On Error Resume Next
        Set rngCopy = Intersect(.Offset(1).SpecialCells(xlCellTypeVisible).EntireRow, Columns("U"))
        On Error GoTo 0
        .AutoFilter
    End With
    
    If Not rngCopy Is Nothing Then
        rngCopy.Copy
        rngDest.PasteSpecial xlPasteValues
        Application.CutCopyMode = False
    End If
    
    Set rngDest = Nothing
    Set rngCopy = Nothing