Below is a table from Cornell on tomato varieties and disease resistance. The real trick is to find a tomato that is disease resistance and tastes good. there a three strains of fusarium so it helps to know which strain you have. Many tomatoes have fusarium resistance but not to all strains. Some that do don't always taste good.
Celebrity is a commercial variety with good disease resistance it is ok as a slicer but not great. Big Beef and husky had good resistance. Sweet 100 cherry, gold nugget was resistant and sweet, Rutgers has been around a while, it is not a large tomato but has good disease resistence. I had new big dwarf, the tomatoes were great but it is determinate and I planted early so I did have any problems with fungal disease. Where I live it is humid most of the time, so if tomatoes can get past the mildews here, they do ok. All of the Hawaii varieties including Kewalo have very good resistance to TMV, three strains of fusarium and verticillium wilts. The skins are tough though, but they should be ok for sauce.
Other than that if you have such severe infections, it is important to keep up with the sanitation, fertilizing to make sure the plants are vigorous and careful watering. You may have to institute a prophylactic fungicide program when conditions are ripe for fungal growth.
It may actually help to rotate your crops to reduce the spore counts. That means not planting anything in the solanaceous family, eggplants, peppers or tomatoes and alternate hosts which are some weeds and strawberries. The fungus is soil borne and persists in crop residues.
You could try solarizing the soil to try to reduce the pathogen in the soil.
Since this is in a community garden and you don't know what diseases the other plants in the garden have, looking for a resistant cultivar and prophylactic sprays are probably your best bet.
https://vegetablemdonline.ppath.cornell. ... Table.html