You can't do it with Autofilter, but you can with Advanced filter.
There are two ways:
1.
Set up a cell somewhere, say cell L1, and copy/paste the header auxiliary column to it.
In cell L2 type an x
Go back to selecting a cell somewhere in the table you want to filter and click Advanced next to Filter (Autofilter) in the Data section of the ribbon.
It should automatically select the table you want to filter. Opt for filtering in place, and for the Criteria range select cells L1:L2, and click OK.
Now you can delete the auxiliary column (and the criteria range if you want) without upsetting the filtering of the table.

2.
Set up a cell somewhere, say cell F24, which has a blank cell above it.
Type this formula into it:
=A2="x"
Go back to selecting a cell somewhere in the table you want to filter and click Advanced next to Filter (Autofilter) in the Data section of the ribbon.
It should automatically select the table you want to filter. Opt for filtering in place, and for the Criteria range select cells F23 (a blank cell) and cell F24 (with the formula in it) immediately below it, and click OK.
Again, you can delete the auxiliary column (and the criteria range if you want) without upsetting the filtering of the table.