I double checked with our team on this one, and they said when a photo is taken, the orientation of your device is captured and encoded into the file. This is what determines whether or not the photo is displayed vertically, or horizontally. When you upload your image to Patreon, our system reads that data to determine the orientation of the file.
If you’re finding that the image isn’t displaying in the way you’d prefer, you’ll need to rotate the file using image editing software before uploading it to Patreon.
Here’s an article that others have found helpful in the past: http://www.mandolincafe.com/forum/entry.php?713-Why-is-my-picture-turned-sideways
And here’s free editing services you can use online: Adobe Spark
I hope this helps!