Soil acidity can be caused by excessive rainfall, fertilizers and the decay of organic matter. The result is soil that is lacking in calcium yet abundant in more toxic elements--making it difficult for crops to grow. The majority of vegetables, beans included, are going to grow best at a barely acidic to neutral pH of 6.5 to 7.0. To help your garden be less acidic for growing vegetables, add lime or wood ash to your soil. In the meantime, some beans will be productive at a pH as low as 5.5 for a vegetable crop, animal feed or cover crop.
Soybeans will grow in acidic soil with a pH as low as 5.5. Soybeans are grown as a vegetable to be eaten as is, or they are processed into bean curd, oil or other soy products. Soybeans are also commonly used as animal feed.
Cowpeas, or black-eyed peas, are also a bean which will grow in acidic soil. Cowpeas will be productive in soil with a pH of 5.5 but prefer a pH of at least 6. Cowpeas are grown as a vegetable, a cover crop and as fodder.
Fava beans will grow at a pH of 4.5 to 8.3. Related to vetch, fava beans are a common bean used for green manure--crops grown off-season to control weeds as well as to be tilled under to improve the nitrogen content of soil. Fava beans are also grown for human consumption or as fodder.