They appear to be snake handlers. The picture also appears to be from the late 1930s.
I'd date it somewhat later. Probably mid 1940s, maybe shortly after the war. The guy at right is missing an arm, maybe from the war or possibly from a coal-mining accident (Appalachia).
Looks more like a timber rattlesnake than an eastern diamondback.
Note the tattoo on the wrist of the guy at left holding the snake. Note also the perspiration under both arms. Long sleeves but the lack of any apparent heavy coats (the woman has a coat, but it's not heavy) suggests either spring or autumn. Woman's dress is more suggestive of autumn. However, either they have the heat really cranked up (probably unlikely, these are poor people) or it's still warm enough to produce the profuse perspiration. Some perspiration might come from the snake handling, but probably not nearly that much, so it's still warm enough for the weather to produce some heat.
I'd say probably Pentecostal Church of God, timber rattlesnake, mid to late September day, in a small coal-mining town, hills of eastern Kentucky, mid to late 1940s.
Almost certainly a timber rattler. Appalachia is the heart of timber rattler country, well out of eastern diamondback range. If it were an eastern diamondback, it would have to have been imported from close to the east coast, which is highly, highly unlikely.
Timber rattler it is, then. :-)