Cornell's veterinary college explains the life cycle of T. gondii:
When a cat ingests an infected prey (or other infected raw meat) the parasite is released into the cat's digestive tract. The organisms then multiply in the wall of the small intestine and produce oocysts during what is known as the intraintestinal infection cycle. These oocysts are then excreted in great numbers in the cat's feces. Cats previously unexposed to T. gondii will usually begin shedding oocysts between three and 10 days after ingestion of infected tissue, and continue shedding for around 10 to 14 days, during which time many millions of oocysts may be produced. Oocysts are very resistant and may survive in the environment for well over a year.
So any single particular cat will spread T. gondii for 10-14 days, but the areas where that cat defecated during that infectious period should be considered infectious for well over a year.
How likely a random (i.e. a new feral moving into the neighborhood) cat will be shedding oocysts when it defecates in your garden depends on your worldwide location. The Companion Animal Parasite Council states:
Prevalence of oocysts (fecal stage) in cats in the United States is
quite low. At any point in time, approximately 1% of cats have
intestinal infection and will be shedding oocysts. In six surveys from
different states in which more than 10 cats were included in all
studies, oocyst shedding ranged from 0.0 to 6.6% (mean of 0.7%).
Much higher prevalence of oocyst shedding has been cited from other
countries, (e.g., 17% in Czechoslovakia, 20% in Brazil, 23% in Costa
Rica, 40% in Turkey, 41% in Egypt).
The Canadian Centre for Occupational Health and Safety states that people involved in the following activities have a higher risk for toxoplasmosis than people not engaged in such activities, but they do not quantify the risk.
Toxoplasmosis is an occupational risk for:
- animal care workers including breeders, keepers, zoo attendants, veterinarians or their associates
- slaughterhouse workers, meat inspectors, line processors, butchers or cooks
- agricultural workers
- landscapers and gardener
- laboratory workers
- health care workers
This risk can be mitigated for hobby gardeners by taking simple steps such as wearing gloves, always washing your hands after gardening, and not eating/drinking while gardening.
To be clear, staying away from feline fecal matter (or soil that could potentially be exposed to feline fecal matter) is not a guarantee that you will not contract toxoplasmosis. Many of our meat animals and farm fields are also exposed to this parasite. Proper washing of food/utensils and proper cooking (or extended freezing) of meat is required to kill the parasite.