Radiation, no. Too random. But hey, we're not talking about humans here, so let's play with this... in spite of the
science-based tag, probably.
In our own world we have numerous examples of multi-stage life forms that pass through two or more forms after birth to adulthood. Tadpoles grow legs and lose their tails to become frogs. Dragonfly nymphs moult several times, the last time revealing their wings. Eels go through up to 4 different metamorphoses during their life cycle. And so on.
Interestingly, not all animals capable of metamorphosis do so purely on biological timers. Sometimes the transformation only occurs due to environmental factors.
Let's assume that some time in the ancient past of your world the proto-humanoids were just such a creature. They start out as a vaguely ape-shaped creature and remain that way until they encounter the environmental factor that stimulates a gland to produce the hormones that start their transformation to adulthood. The stimulus is fairly common in plants of their world, but over time they evolve to a nearly symbiotic relationship on a particular family of plants. Only by consuming the sap of the plants in that family will their final transformation begin.
As their transformation stimulus becomes more specific they also evolve to become fully fertile during their 'juvenile' stage. They no longer need to transform to continue their species. This new strain is less reliant on the plants because they can breed without them. They continue to develop until the local equivalent of H. Sap. becomes the dominant intelligent species of the planet.
But somewhere in their heads there is a tiny group of cells, a small gland that looks like part of their endocrine system but doesn't seem to have any real purpose. Nobody really knows what it does.
Until one day some explorer finds a small plant with an interesting smell and starts eating it. He falls ill of course, and when the fevers pass he has changed. Maybe he has new parts, maybe some of those old parts that everyone thought were just atavistic left-overs from their evolutionary past become enlarged and fully functional again. Their endocrine balance shifts and so on.
So he gives the plant to someone else and it kills them, because their genetics are too far off the original line. In fact it turns out that only a small percentage of the population actually has suitable genetics to survive the transformation process, he was just one lucky S.O.B.
70% are lacking the genetic sequence that codes for iodothyronine (or whatever hormone you like) production or some other blocker and nothing happens. 20% go through the transformation with varying degrees of success, including the few full transformations.
And the other 10%, unlucky sods that they are, die in screaming agony as the transformation goes out of control and destroys their bodies.
So... 1 in 10 chance of agonizing death.
Et voila, an 'intelligent' species with a reason to do something stupid that's probably going to do nothing but could make them much better than other people. Or kill them horribly.
No radiation required. :)