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You shouldn't kill them by transplanting the at that stage. Looks like enough soil between them to keep the roots covered. Just be quick to eliminate air exposure time. Have your pots or holes ready to go then carefully with a large table spoon cut the soil around each sprout. Most likely it will stunt the growth for a few days but hopefully no real harm done.
But honestly, I think i would just leave them in like that. Grow 3 in a cluster, it has been fine in the past for me. Just keep the clusters spread apart a good distance, because they can become huge looking bushes! When big enough i have tied the plants off to the side to give each plant in the cluster optimum sun in da middle.
I have never heard or saw such a problem or had any such problems with root tangling or whatever. I have however grown many plots with 3 plant in one cluster like yours and have never had any problems. You can separate them if you like, they are young enough that transplanting should only stunt them for a week or so. The trick to growing clusters like you have is to start tieing them to the sides once big enough so the center of the cluster will get good sun. Just throwing you some ideas of what has worked for me in the past.
Ohh, 1 more thing. Your grow area looks like my old grow spot. And animals were a real pain with my crop. Raccoons and skunks would dig some of them up looking for grubs in fresh soil, leaving them dead. The deer would munch off the leaves and top my crop every couple weeks. So invest in some kind of barrier, chicken or bunny fences works wonders. The spot you picked is also probly a watering hole and bedding area for deer or whatever kind of critters are in your parts.