Are there alternatives to cypress and pressure-treated pine for fences?
There are good alternatives to cypress and pressure-treated pine for your privacy screen, especially if you look at a planted hedge, or fence components made from nonwood products.
Have you considered a living hedge? If you are considering a vegetable garden, you must have good sun exposure. Inkberry (Ilex glabra)—for a clipped hedge—or Southern wax myrtle (Myrica cerifera)—for an informal (not clipped) hedge—are two southwest Florida natives that will form a dense evergreen hedge. If you are concerned about small animals getting into your garden, or pets escaping, install a wire-mesh fence and plant the shrubs on either side of the fence, staggering the rows from one side to the other. The shrubs will quickly grow together and completely conceal the fence.
Another option would be to grow vines on a wire-mesh fence. Indigenous vines such as Southern honeysuckle (Lonicera sempervirens), Carolina yellow jessamine (Gelsemium sempervirens), trumpet creeper (Campsis radicans) or Virginia creeper (Parthenocissus quinquefolia) will grow into an effective evergreen screen. You could also plant cucumbers, peas, gourds, or grapes on the trellis, or espalier currants, oranges, lemons, etc.—turning your property into an efficient permaculture garden.
If you prefer a constructed fence, there are good alternatives made from recycled materials or manufacturing by-products. These construction materials tend to be relatively maintenance free, durable, and do not need to be stained or painted. Trex is one company that has a line of products for decking and fencing. There is another product called Prairie Picket made from recycled plastic and wheat straw that looks promising. Or—right in Florida (local is better)—there's American Fence Company, making fence components out of recycled plastic.
Sustainability comes into play not just in how a product is manufactured, what materials it is made from, or how far it must be transported. Another important factor is durability—how long something will last. Build something that will stand the test of time.