These species are known as invasive because they can out compete the native plants and animals and possibly change the ecosystem. Some people would argue that you should try to make your yard as natural as possible and only grow native species. Other people like the appearance of a green, tidy, carefully tended lawn. In Florida, this type of lawn might contribute to ecosystem degradation if non-native plants spread seeds into natural areas. Ecosystems can also be affected by excess fertilizers which causes algae to grow in estuaries or drainage ditches.
Nitrates can contaminate the groundwater, and lawn irrigation can lower the water table.
Unfortunately, many people smuggle these animals to sell as pets. This problem is compounded when these animals are released into the wild. There are some plants and animals that were introduced so long ago that we think of them as natives. For example, dandelions came from Europe. Nearly all of our food crops and livestock came from plants and animals native to some other country.