BlueJay77 is by far the true and real expert on Beans here.
You might want to send him a private message thing.
But what the others have said, Beans very very rarely cross pollinate.
Cross pollination naturally of a whole garden crop, every single pod, well, not sure if that has ever happened in the history of the world.
What happens when you plant some varieties in with some other varieties is that the plants of one variety will grow much stronger than the other variety, so that one variety may produce much more than the other, and yet if the 2 varieties had be planted well separated even that much less producing variety might well produce as well as the other one.
Each variety of Bean has different plant vigor. Until it's checked on that they do well together, Beans should not be planted mixed. If you are going to plant them mixed, give them extra space, and make sure they are separated as to pole, bush, half runner, tender pole, or viney growth types. Even bush types have several growth patterns.
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I suspect most or all of your kidney beans did not sprout, and or, something happened to the plants.
Just to be on the hopeful side, did any of your pinto Beans look different? A normal thing that happens with some varieties is sometimes a bean will show up that is mostly the darker color on it. Sometimes, but not very often, the darker bean will "breed true". I think that is from normal selection and does not involve cross pollination usually.
Other times a bean will appear for the bean seed saver who grows many varieties that is a surprise. One plant in among a variety making dry beans differently than the rest.
You see, cross pollination does happen in Beans. Something like maybe out of a thousand pods. But you don't know it! Usually!
Couple years ago one of my Mayflower bean variety plants made some bean seeds at least 3 times as big as the normally smallish bean seeds they make. I packed those separately in an envelope. Then, last year I planted the seeds from that pack figuring, may as well plant these because i only want this many plants anyway, plus let's see if i get a strain of mayflower bean with big seeds. 2 of the plants made normal mayflower plants, pods, and seeds.
One of them though... made a different growing plant, a nice pole, dry bean type pod, not the basically cutshort pod type of mayflower, produced in flushes, then waited and made a few more at late season's end. The beans, they are medium sized, regular bean shaped, slightly flattened, white of the shade and texture of mayflower's unusual texture, not a hint of red or rose on it, but instead, a subtle spray of soft black from one end, very subtle. It has the look around the eye, called the hilum, of Hutterite, a very good bean, which had been growing near the mayflower several years back.
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So, I'm still not sure if cross pollination directly shows up soon as it happens and the bean ripens. Maybe the mechanism of the bumblebee or cutter bee tearing into the flower causes only one bean to develop? Or just a few, so the ones that develop have a chance to be bigger??? I don't know.
I do know that if you are looking for suspected cross pollinated beans, and if you grow enough varieties of beans, eventually you will find them!
I have a few other suspected crosses, but I have to check first.
If you saved your pinto seeds, sort through them for any that are extra or even abnormally large. Also, sort through for the darkest and lightest ones.
Now plant each of those separately from each other WELL MARKED AND LABELLED and see if they "breed true".
THE APPLE DOES NOT FALL FAR FROM THE TREE
Anything that BlueJay77 says that is different than what I said, go with what BlueJay says. He is so much more experienced than I am. I would only qualify as his assistant.