At the moment the Owl Carousel autoHeight works only with 1 item on screen. Their plan is to calculate all visible items and change height according to highest item.
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I'm not sure if anyone is still looking for solutions for this problem in 2020, but after trying a lot of things that didn't work, I found a very simple one. It's all about setting no height to the item that's not active.
Like so:
.owl-item {height: 0;}
.owl-item.active {height: auto;}
It's elegant and no javascript is needed. You can even play with transitions to set some cool animations.
I hope I have helped someone here.
PS: To use this method, keep autoHeight: false ... otherwise the carousel height will be set to 0 by the library