First off, with use of traits (if this system continues from New Vegas), the process can be kicked off. After all, it could be a genetic twist of fate that caused people to become a ghoul with high doses of radiation, as opposed to dying a painful and prolonged death. Unless you take this trait, you get affected by radiation as anyone else.
Perhaps this trait (offering minor radiation resistance, traits tend to be minor stuff after all, and as a counterbalance, there's just something off about the person with this trait that causes people to shy away from him/her, perhaps a minus to Charisma). Having this trait would open up the ability to take Ghoul restricted perks, which could lead to becoming a Glowing One variant of Ghouls. Of course, becoming a Glowing One would cause some problems, after all you'd be positively radiating; so the limitation would be that you'd have to wear environmental suits and armour that would normally protect the wearer from radiation to protect others. Then again, Jason Bright didn't seem to harm the player character (as in bringing up the Rad count), and most other Glowing Ones you'd encounter are Feral, I'd assume the radiation is an AoE attack that's centred on the Glowing One.
Maybe a further hit to Charisma for being a Glowing One would be in order.
All Charisma penalties should be nullified for those who are Ghouls, Super Mutants, those who aren't disgusted/afraid of Ghouls.
Ghouls have a higher Endurance than humans (radiation resistance, like other environmental resistances are tied in with Endurance) which also gives them a resistance to chemicals (remember the Sugar Bombs mission in Fallout 3?).
Another trait they have is healing when being irradiated, so drinking irradiated water, eating irradiated food, standing in a radioactive area would regenerate Ghoul characters.
There was a bonus perk if you got radiated enough in one of Moira Brown's missions in Fallout 3, where your critically wounded limbs can get a regeneration buff when your Rad levels increase, so this would be an extension of this Perk, and then some.