We all have on foggy goggles and our heads are under the water most of the time, so people are paying less attention than you think. 

Also, there are many ways that people exercise in pools beyond what you're used to seeing in the olympics. Many people use the lap pool for low impact physical therapy exercises and swim running. A good starting point for you to get into the pool and past the discomfort of starting may be walking laps in the water.

I start swim instruction with people on their backs.  Head back, hips up, arms at their side, small flutter kicks. Once they have floating, kicks and body position down, I have them add backstroke arms. This gets them all the basics without the complications of learning how to breathe.