I spent over thirty years flying airliners with contact lenses. There is no issue. As stated, you will be limited to flying with a spare pair of prescription glasses and take note that photochromic lenses are not allowed. If you want sun protection on your back up's then buy clip on sun covers.
Interestingly as the years increased I found myself needing reading correction on top of the lenses so bought a good pair of sunglasses and then attached +1 diving mask correction lenses. These serve me well to this day and my AME is happy that they are simply the same as using reading glasses (which is allowed as well) on top of the lenses. Note though that if purchasing diving mask corrector lenses that they are of a flexible type. I spent a lot of money in Florida years ago buying some that when I got them back home to the UK were actually rigid and flat. That meant they could not accommodate the natural curvature of the sun glass lens and were useless.