Most optometrists and ophthalmologists agree that showering with your contact lenses in is fine if you take precautions to not get water in your eyes. The Centers for Disease Control and Prevention and the Food and Drug Administration warn that it's best to avoid showering while wearing contacts because there are several risks associated with getting tap water in your eyes.
The American Optometric Association recommends that you "remove contact lenses before swimming or entering a hot tub" but doesn't oppose showering while wearing contacts.
The Centers for Disease Control and Prevention and the Food and Drug Administration recommend removing contact lenses before any activity involving contact with water, including showering, using a hot tub, or swimming."
Why is Water Bad for Eyes?
The water in your shower may contain microbes or other impurities that can cause eye infections.
Why is Water Bad for Contacts?
The AOA warns against using tap water as a storage or cleaning solution. Unlike buffered saline, it can change the shape of your contacts so that they do not fit your eyes correctly.
Contact manufacturer CIBA Vision gives guidelines for showering while wearing contacts:
Close your eyes while rinsing your hair or face. If you get water or soap in your eye, remove, clean and disinfect your lenses. Contact your eye care professional if you experience persistent pain or redness.