Is it ok to stack LPs horizontally?

To the original question - NO.

LP records are thicker in the middle. Some outer edges are thicker than others, but generally, not as thick as the centers (labels, etc.). So, stack 'em like pancakes and they will sag and not uniformly - they warp. The warp sends a very low, sub audio, frequency into your gear, drives it nuts, keeps changing the VTA (relationship between the stylus and the groove walls) and generally makes a mess. Besides, how are you going to pull out that favorite disk you havent played in a few years when there are 57 records piled on top of it? Stay vertical, friend.

Most turntables play slightly warped LPs fine. What they cant play are compressed recording grooves. LPs weigh a ton. Storing them flat can press the groves. vertical is the only way to go.

In addition to warping (which I never considered) I always thought that the extra weight of storing horizontally would cause dust and dirt to be pressed into the grooves. So I always store vertically. 

@heretobuy      Goodness, that rig looks highly unstable on its tiny angled feet.  Anyone who has lifted that number of LPs knows how heavy they are.

A dog or a small child could accidentally knock it over and the falling LPs cause injury or worse.  I wouldn't have it in my house.