In a perfect world, we should be able to achieve this using the CSS user-select
property. Unfortunately, browser support for this feature is inconsistent and limited. In my own experiments, it seems to prevent the ability to select text visually, but does not stop images from being dragged. As a temporary solution, you may need to employ a workaround such as utilizing background-images, like demonstrated above.
For those curious, you can implement the following code to disable selection for all text elements within the body, or apply it selectively to specific elements to prevent selection/dragging:
body {
-webkit-touch-callout: none;
-webkit-user-select: none;
-khtml-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}