Use Photoshop scripting to adjust any image that exceeds Instagram aspect ratios by padding the canvas size with white background color.

InstagramAspectPadding.js

var docRef = app.activeDocument;
var currentWidth = docRef.width;
var currentHeight = docRef.height;
var aspectRatio = currentWidth / currentHeight;

var mycolor = new SolidColor(); 
mycolor.rgb.hexValue = "ffffff";
app.backgroundColor = mycolor;

if (aspectRatio < 0.8) {
    var paddedWidth = currentHeight * 0.8;
    docRef.resizeCanvas(paddedWidth, currentHeight, AnchorPosition.MIDDLECENTER);
} else if (aspectRatio > 1.91) {
    var paddedHeight = currentWidth * 1.91;
    docRef.resizeCanvas(currentWidth, paddedHeight, AnchorPosition.MIDDLECENTER);
}