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.
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.