It’s a round peg in a square hole. Printed postcards have rectangular pictures and Instagram has square pictures.
If you use any of the PostCard apps that offer to print and mail the card you create I have talked about in the past, you get a post card with your image centered on it. Not exactly what people would expect for a print postcard they are used to seeing.
You can re-size the image on the page to fill it out side to side but then you loose the top/bottom:
It’s no fault of these apps, they just hadn’t planned for Instagram square images.
New to this group of apps that offer to print/postal mail your creations is Postagram. This free app allows you to create a postcard using your Instagram square photos, which they will print and mail for you. As you can see, they don’t print the image across the whole card, but they make it so a person can pull the image out of the card to use just it.