This is called the "Cell insertion menu". Its appearance is defined in MiscExpressions.tr via the front end resource "CellInsertionMenu".

Notebooks (depending on the stylesheet, of course) have it defined as a "cell insertion point cell" by default:

AbsoluteOptions[SelectedNotebook[], "CellInsertionPointCell"] (* -> {CellInsertionPointCell -> FEPrivate`FrontEndResource["FEExpressions", "CellInsertionMenu"]} *) 

We can disable it as follows:

SetOptions[SelectedNotebook[], "CellInsertionPointCell" -> Cell[]] (* gone *) 

I guess you can also remove this option from the stylesheet.

This is called the "Cell insertion menu". Its appearance is defined in MiscExpressions.tr via the front end resource "CellInsertionMenu".

Notebooks (depending on the stylesheet, of course) have it defined as a "cell insertion point cell" by default:

AbsoluteOptions[SelectedNotebook[], "CellInsertionPointCell"] (* -> {CellInsertionPointCell -> FEPrivate`FrontEndResource["FEExpressions", "CellInsertionMenu"]} *) 

We can disable it as follows:

SetOptions[SelectedNotebook[], "CellInsertionPointCell" -> Cell[]] (* gone *) 

To kill this pop-up at the Stylesheet level one may use Edit Stylesheet and insert:

Cell[StyleData[All, "Working"], CellInsertionPointCell -> None ]