By default, the move tool in GIMP moves the uppermost layer that has a non-transparent pixel at the click location. Text layers tend to have many transparent pixels, and thus it is easy to grab a layer behind them (that is, lower in the layer stack). The same would happen if you had a few thin lines on an otherwise transparent layer.
What you can do:
- Make sure that you click on a pixel of the text, or
- Switch from the Pick a layer mode to Move the active layer mode
The latter is what holding the Shift key accomplishes. You can see this mode in the move tool options:
You can also change the default there - switch to Move the active layer mode with the mouse and save the tool options. Then holding the Shift key will switch to Pick a layer mode.
You can also move the text layer with the text tool.
Hold the Alt key and drag the layer with the text tool. If your window manager or desktop environment uses Alt+Drag for its own purposes, you can use Ctrl+Alt and drag.
You might want to change this in your WM or DE configuration, as Alt is a frequently used modified key in GIMP.