Create Lists for Drop-Down Menus in Different Sheet
This will be hard to get right without the actual workbook. 


Stop adding and removing Sheets("Filter Builder"); just hide it.  
Avoid Select or Activate. Reference: Excel VBA Introduction Part 5 - Selecting Cells (Range, Cells, Activecell, End, Offset) 
By working with the data in arrays, you can avoid filtering &amp; unfiltering you data as well as hiding and unhiding the columns.
Use With block to qualify your ranges. Reference: Excel VBA Introduction Part 12 - With Statements
Replace your static ranges ,e.g. .Range("$A$1:$AF$5150"),  dynamic ranges ,e.g. .Range(.Range("A" &amp; .Rows.Count).End(xlup),"AF1"))


Here are some inconsistencies


The initial ActiveSheet, Sheet2 and Sheets("Checklist Builder") all appear to be the same Worksheet.  Pick 1 and use it in a With block. (e.g. With Sheet2)
Range("$A$1:$AF$5150").AutoFilter - .Range("$A$1:$AF$150").AutoFilter




This should work "As Is" but it is hard to say without the actual Workbook.  You will have to add a Worksheet, name it "Filter Builder", hide it and forget about it.  I would guess that it should take less than 1 sec to execute.  

Sub Macro1()

'TURNS OFF THE SCREEN UPDATING SO IT BRING YOU TO THE FILTER OPTIONS TAB AFTER THE MACRO IS COMPLETE
    Application.ScreenUpdating = False

    Dim data As Variant, results As Variant
    Dim count As Long, x As Long
    With Sheets("Checklist Builder")
        data = .Range("$A$1:$AF$5150").Value
        ReDim results(1 To UBound(data), 1 To 2)
        'Fill array with the values
        For x = 1 To UBound(data)
            If count = 1 Or UCase(data(x, 7)) = "SPECIAL VALIDATION" Then
                count = count + 1
                results(count, 1) = data(x, 7)
                results(count, 2) = data(x, 8)
            End If
        Next
    End With


    'DELIMITS THE DATA SO THE TEXT SPLIT UP IN TO DIFFERENT COLUMNS, DIVIDED UP BY COMMAS

    With Sheets("Filter Builder")
        .Cells.Clear
        .Range("A1").Resize(UBound(results), UBound(results, 2)).Value = results

        .Columns("B:B").TextToColumns Destination:=Range("B1"), DataType:=xlDelimited, TextQualifier:=xlDoubleQuote, ConsecutiveDelimiter:=False, Tab:=False, Semicolon:=False, Comma:=True, Space:=False, Other:=False, FieldInfo:=Array(Array(1, 1), Array(2, 1), Array(3, 1), Array(4, 1)), TrailingMinusNumbers:=True

        .Rows("2:1150").Copy
        Sheets("Filter Options").Range("K1").PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks _
                                                                                                   :=False, Transpose:=True
        Application.CutCopyMode = False
    End With
    Application.ScreenUpdating = True

End Sub