One important thing you are going to need in order to make cultured non-dairy foods at home is a fermentation station. You will need a place that safely gets predictably hot for a consistent length of time. You can do this really cheaply or quite expensively. I’m putting pictures and links here, but I am NOT affiliated with any of the companies listed. I’ve done some research and am jotting down some ideas that I’ve never tried.
You will also need a reliable thermometer to measure the temperatures in your station.
Oven-Many of the newer ovens have a temperature setting that will go down to 100 degrees. You will need to make sure that the setting matches the actual temperature in the oven (my oven is suuuuuper old and doesn’t match) but I have heard multiple folks say they can use their oven to ferment cheese and yogurt.
Crock pot-If you turn it on low and leave the lid off, some crock pots will hold around 100 degrees. Test it first by filling it with water and checking the temperature of the water after an hour or so.
Instapot-If you’ve spoken to another human being in the last 6 months, you’ve probably heard about the Instapot. You can make yogurt in these easily, though they are on the pricey side. I’ve never used one personally, but I would definitely get one, if I didn’t already have a pressure cooker and a crock pot and a yogurt maker.
Light bulb in the oven-I tried the light bulb in the oven trick, but my oven only got to 80 degrees. This is hot enough to culture non-dairy milks a little bit, but will not do the job completely. Soy yogurt will remain runny-ish. I used a 53 watt eco-bulb, and my stove is made in the 1930’s. If you want to try this one with a higher watt bulb in a newer, more airtight oven, you may be able to hit 100 degrees.
Heating Pad in a box-This method worked great for me. I got a wine box from Trader Joe’s (not too big) and I wrapped it in a chenille blanket. I put the pad on high and it stayed at 100 degrees for many hours.
Yogurt Maker-I’ve found yogurt makers at Goodwill, but you can also pick them up new pretty cheap online. I dislike many of the yogurt makers available because I make bulk amounts of yogurt and often these makers only fit small jars. There are exceptions to this rule, however, like the one I linked to above, which apparently comes with a component for thickening the yogurt as well!
Brød and Taylor-I have a Brod and Taylor and it works great, though it is expensive. It will fit massive amounts of milk for culturing and the temperature is adjustable.
Dehydrator-dehydrators can be made to reach low temperatures for long periods of time. I haven’t used one for this purpose, but I’m told that the Excalibur can be used for yogurt and cheese making purposes.