I think the Enclave would be the real wild card, aren't they always. So lets save them for last.
The Responders, are ill equipped to handle the dragon like Scorchbeasts...or just beasts I suppose without the carried infection. However, Responders are one of the most beneficial groups for the wasteland that could have been possible, and honestly the idea that surviving members of civil services would band together for the benefit of the communities they served is one of the best ideas to come out of 76. It's hard to believe how little we've seen this theme explored in the past.
Surviving first responders, as the name implies, they not only have access to various avenues of training from weapons handling and first aid to an innate knowledge of the area that comes from being dispatched to thousands of calls across the area. With Appalachia being relatively unscathed, perhaps only the Mojave fairing better out of locations seen thus far, a group like the Responders would be invaluable for the continuation of society.
And looking at all the progress they made in spite of the scorch horde, I have no doubt they would have been instrumental in rebuilding the area. Their scientists were ultimately able to create the vaccine; they educated settlers across the region to survive the conditions; and they held several key positions like the airport. Given their ability to withstand or outsmart the scorched, I have no doubt they would have been able to handle the various super mutants or other hazards. If anything it would have been relations with other human groups which would have given them the most trouble.
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With Tagerdy's BoS, there were existing tensions with the Responders, but they were almost all due to the presence of the Scorch. And a none of the audio logs or terminal entries make the BoS out to be an unnecessary bundle of dicks. At the time, they were still more military than paramilitary, so I seriously doubt they would be instantly hostile with the Responders given similar themes of civil and military service.
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The preppers would have certainly been troublemakers, as many core tenants of their paranoia would have them at odds with both former police and former military. I have no doubt they would have forced a confrontation of some kind with either or both of the other two positive factions.
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And then there's the Enclave. It seems likely that the internal turmoil within the bunker would have happened regardless of the scorch or not. Eckhart was a real son of a bitch. And the field operative, whose name escapes me, was killed in a deathclaw den not by the scorch. So the bunker and all its facilities would have been there for an unimpeded BoS to recover.
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In the long term I suspect we would have seen a rise of an east coast nation strong enough to rival that of the NCR out west. The biggest impact remains naming the monster though because without the Scorch, we would need most is a name for those big bastards. lol