There are many many areas in Belize that you can swim directly off the beach or the boat and not have to step on sea grass (known as turtle grass, manatee grass, and shoal grass). I personally love seagrasses because of the many surprises it holds...lobsters molting, sea turtles and eagle rays feeding, and without it, manatees wouldn't have a place to graze.
Most folks paranoia over seagrasses are unfounded - and in most areas you can swim over it without touching it at all. Seagrasses are an integral part of the reef environment and without it, all those colorful fish that you see there would not have a place to to hide and feed while they are growing up to face the "big boys" on the reef.