Q.Pruning/Shaping Green Giant Arborvitae
I prefer not to regularly sheer Green Giants as it diminishes the plants natural shape and texture. Trouble is, as the tree matures it can get a bit leggy and start to thin down below which diminishes its value as privacy screening. Is there any downside to lightly shearing green giants every couple of years in the fall to help with thickening and cross branching? Tx!

Certified GKH Gardening Expert
You can. Just make sure that you do not cut off the top of the shrub. This will break its conical shape. There are a few things to consider, as well. IF they are planted too closely, then they might get a little more leggy than you want. Also, the closer to full sun that you can get, the less they will stretch in search of light. As long as you are providing the right conditions, and only do maintenance pruning, you should see a healthy shrub.
https://www.gardeningknowhow.com/ornamental/trees/arborvitae/growing-arborvitae-trees.htm