I think the main issue with your formula is that you cannot use table references in the data validation.
Don't ask me why. I think it is just an outstanding Excel bug which hasn't been fixed yet. Please see this link for further info: https://exceloffthegrid.com/using-an-excel-table-within-a-data-validation-list/
The best way I have found to work around this is to create a named range which refers to the table references you need ("Material_List" and "Material_List[#Headers]" in your case). Then you can use those named ranges in your data validation instead of the table references directly.
However, I think there are also other issues with your formula. For example, this part:
MATCH(Material_List;$B50;0)
Normally a MATCH would be in the format of:
MATCH(<single value to look for>, <range to look in>, 0)
You appear to have that reversed, meaning that it should always return a #VALUE! error.
Also, I don't think you can use match on a 2D array, so if your "Material_List" table is more than a single column, that would also cause it to return a #VALUE! error.
UPDATE:
The way I would tackle dependent dropdowns would be as follows.
I would create a "Material_List" table similar to below (could be on a hidden sheet):

Then I would create 3 named ranges.
One for the table body range, called "MaterialList_TblRange":
=Material_List
One for the table header range, called "MaterialList_TblHeaderRange":
=Material_List[#Headers]
And one to refer to the dependant dropdown options, called "DropDownOptions" (this is by far the most complicated part):
=INDEX(MaterialList_TblRange,1,MATCH(Sheet1!$B23,MaterialList_TblHeaderRange,0)):INDEX(MaterialList_TblRange,COUNTA(INDEX(MaterialList_TblRange,1,MATCH(Sheet1!$B23,MaterialList_TblHeaderRange,0)):INDEX(MaterialList_TblRange,ROWS(MaterialList_TblRange),MATCH(Sheet1!$B23,MaterialList_TblHeaderRange,0))),MATCH(Sheet1!$B23,MaterialList_TblHeaderRange,0))
I will explain what this is doing in a moment.
The last step is to set up the data validation where we want our lists.
Where we want the master lists to appear, we can simply enter:
=MaterialList_TblHeaderRange
And the defendant dropdown validation can be entered as:
=DropDownOptions
This is the result:

Now back to the long "DropDownOptions" named range formula...
Basically, we use INDEX:INDEX to select the first/last cell in the range we want to use in out dropdown.
The first INDEX:
=INDEX(MaterialList_TblRange,1,MATCH(Sheet1!$B23,MaterialList_TblHeaderRange,0))
Simply selects the first cell from the column whose header matches the selection in our first dropdown.
The second index does the same, except that instead of selecting the first cell in the column, it counts the number of cells that contain text and uses that as the last cell in the range.
This does mean that we mustn't have any gaps in this table, otherwise an option might be missed off the end.
I hope this makes sense.