Numbers is designed to show the row ans column reference tabs when a table is the 'active' table. The table becomes 'active' when you select any cell or the table itself.
The action you describe, command-click, is a system wide instruction to add the clicked item to or remove the clicked item from an existing selection. In this case, where the Table is the single item in the selection, a command-click on the circle toggles that item to 'not selected.'
You can also deselect the table (and all other selected objects) by clicking any 'empty' point on the sheet.
'Headers' and 'Footers' in the context of your comment above refers to Header Rows, Footer Rows, and Header Columns,
These are rows with several properties not shared with regular 'body rows'. Most significant or most useful are that Header rows and columns can be 'frozen' to make them remain visible while any part of the body of the table is still visible, and that cells in Header rows and Footer rows are excluded from 'whole column' range references in many functions, making it possible, for example, to use SUM(B) in a formula placed in a Header or Footer row of column B.
Getting back to the 'problem' of row and column reference tabs popping into view whenever the table is active, I agree that can be a distraction when the table is active only because someone is entering data in a column recognized by it's name in the column header (or in similar circumstances). There's currently no user control available to make that happen, so no one in this user-to-user community is likely to be able to offer a solution.
You can, though, Provide Numbers Feedback, using the menu item of that name, found in the Numbers menu, to make a Feature Enhancement request.
Regards,
Barry