Nope, it's not "incredibly" easy to convert a AR-15 to fully automatic.
Older receivers were easier but still required permanent modifications that made the receiver a "machine gun" in the eyes of the law, with no way to restore it, short of welding (and welding aluminium is tricky).
Modern receivers require machining and quite a number of different small parts to become fully automatic. Now, is that machining particularly difficult? No, but then again, if you have the tools and knowledge to do that, building a fully automatic firearm from scratch is "easy", as it's not particularly difficult to do without such knowledge and tools (the Sten only cost a quid or two to manufacture during WWII for a reason).
So, yes, as an adult you should be terrified as the difference between a semi auto receiver and non registered fully automatic one is ten years in jail and a $100,000 fine. As others have already mentioned, a fully automatic assault rifle isn't measurably more dangerous in trained hands than a semi auto one. The fully automatic fire is only really effective in the assault, to basically provide your own covering fire, and since that tactic a) haven't been popular with infantry forces in the past several decades, and b) is only useful against an armed and prepared opponent anyway (i.e. it's superflous/not applicable in most civilian settings), there isn't really much extra effect to be had from fully automatic capability. (The one semi recent such shooting we've had in Sweden with an assault rifle, the perpetrator didn't actually use the fully automatic capability much. In the more recent Norwegian case, the weapon didn't have any fully automatic capability, and that of course had no discernible bearing on the outcome.
That's of course not to say that its a good thing that crazy people have easy access to capable firearms, but whether your efforts should be aimed at the "capable firearm" or "crazy" that's not at all clear. We have very strict weapons regulations in Sweden, and that obviously haven't had one bit of effect on the recent spree of shootings; with fully automatic AK-47 type rifles that were fired on automatic in one case even. But again it's not clear that the automatic fire had any effect that the same volume of semi automatic fire wouldn't have had. It's as others have said, probably the other way around. (And in China petrol and knives have been used in lieu of a firearm, so there's no simple solution, like the people so singularly set on banning guns would have you believe.)