Shortening of the spine can happen regardless of what exercise you do (or don't). Everything should be fine as long you learn to lead your body with your head, which should be balanced on the atlanto-occipital joint (a little bit behind the soft palate and between the ears). When the head is really balanced, it feels as if you were floating, instead of stiff or dragged down.

When you exercise learn to use the support your skeleton provides, rather than thinking that it's only the muscle's job. Respect all of your balance points of your body from head to foot. We balance mostly at 6 points corresponding to the joints/space between bones.  And after training be mindful of any tension you may have, freeing any tension in your muscles, especially the ones revolving around your spine and head --which in turn will also help the organs, including the tongue to free up. 

When you sit, learn also to balance on your sitbones, so your legs can move freely.

At the end it doesn't matter how strong a voluntary muscle is, when not in action it should be free...and not interfere with the inherent reflexes that we have. Posture/alignment is a job for the deep muscles. 

Also, we decrease height during inhalation and expand during exhalation through minimal compression and decompression of the spinal joints, to support breathing...so the important thing here is that the spine is free to move permanently.

Hope this helps

eddie it shouldnt be harmful if your using proper form

Your spine compresses during the day because of gravity and at night decompresses; these sorts of things are dynamic and not permanent. Even axial loading exercises at a high frequency cannot permanently compress your spine. If anything these types of exercises will help facilitate stronger body integrity/posture. It's important to use correct form however because bad form will only help reinforce bad postures like rounded shoulders and anterior pelvic tilt.

This video sums it up pretty well 

https://www.youtube.com/watch?v=gxmtuD1HylI

tl; dw Have a proper warm up, proper form, stretch, work on mobility, and make sure you don't develop muscle imbalances.

In the comments someone basically answers your question: "Squats won't make you shorter PERMANENTLY. It may compress your spine for a few hours like most activities like running etc can. But after a good night sleep it should be back to normal. So no worries guys.."