In 2.79 you could limit which orthographic views you want to be able to see your image planes for references to be visible from. For example front, side, top, etc. For the life of me I can not find this function in version 2.80. All I seem to be able to find is to completely hide your images from all otho views, but no granular control over which ortho views. For instance, I want my "front" reference image to only be visible from the front otho view. Am I just overlooking this or was this removed in 2.80?
The functionality that is missing would be to see one reference image on every perspective. And yes you can no longer hide the image when you leave the front ortho view.
The easiest possibility is to set up a separate camera in Front-Ortho view and add a background image to the specific camera. If you leave the camera view the image will no longer be visible
To approximate what you want to achieve with a reference image you have to insert the image in "Front" View so the normal is aligned with the y-axis.Looking at the settings shown in this answer:
You have to uncheck "Display Perspective" so it doesn't show up in perspective view, And make sure you have "Front" Selected in the "Side" selector so it is transparent from the back.
You will however always see the outline of the plane.