Answer

Tableau Desktop 2019.2 and Newer Versions 

Go to Worksheet > Uncheck Show Sort Controls 

Tableau Desktop 2019.1 and Older Versions

Use one of the following workarounds.

Option 1: Use a blank dashboard object

1. Create your view, and place it on a dashboard. 
2. Select "Floating" from Objects in the left pane
3. Select Blank and place this object in the dashboard. 
4. Resize and move this pane to cover the headers you would like to prevent from being sorted. 

Option 2: Create a separate "Headers" sheet.

Step 1: Create the view

1. In Tableau Desktop, connect to Superstore sample data.
2. Drag Category to Rows.
3. Double-click Profit.
4. On Show Me, select horizontal bars.

Step 2: Remove headers

1. Right-click Category on Rows, and clear Show Header.
2. Right-click the x-axis, and then select Edit Axis.
3. In the Edit Axis dialog box, select Fixed, copy the value in End, and then click OK.
4. Right-click Profit on Columns, and clear Show Header.

Step 3: Create a headers sheet

1. Select Worksheet > New Worksheet.
2. Drag Profit to Columns.
3. Drag Category to Filters, click All, select Exclude, and then click OK.
4. Right-click the x-axis, and then select Edit Axis.
5. In the Edit Axis dialog box, select Fixed, paste the End value copied previously into End, and then click OK.

Step 4: Create a dashboard

1. Select Dashboard > New Dashboard.
2. Drag both sheets onto the dashboard such that the scales align.
3. On Sheet 2, right-click the title, and then select Hide Title.

Additional Information