A "Carrington-level" event nowadays would most likely be much less disruptive, as back then all the early radio and spark gap stuff was well under 50 MHz, which is where almost all of the natural noise winds up in the spectrum. Ever notice, for example you can hear your shaver motor on an AM radio but not an FM one. This is not due to AM vs. FM, (well, it is a little) but mostly due to the fact that AM is about 1 MHz and FM is about 100 MHz, well above the "static line" around 50 MHz.
It would take a much stronger signal than back then to cause the same level of disruption. Not saying that can't happen, but modern radio communications are quite a bit more robust than they were back over 100 years ago.
The concern is not so much about the disruption of radio communications, but the power grid. Our society might not survive a massive, long-term (months or even years) blackout (a huge number of transformers might be destroyed all at once by the induced EMF).