Actors were not like movie stars right so it wouldn't have been like George Clooney shooting Obama. But was he famous enough to be recognized? Were people as surprised that he did it as they were that Lincoln was killed?
In "A History of the Theatre," the author's write about the high level of fame afforded the Booth family. Junius Brutus Booth (John Wilkes's father) was a player at Covent Gardens, one of the most lavish playhouses in England at the time, before eloping to the US.
Edwin Booth, the eldest Booth brother, is considered the most famous American actor of his era. He toured all over the US and internationally with his father, and owned or founded multiple playhouses that are still running today.
John Wilkes and his elder brother Junius Jr. were afforded fame in their own right, but nothing like Edwin's. The only time the three appeared on stage together was a benefit performance of Julius Caesar where Edwin and Junius Jr. played Brutus and Cassius respectively, while John Wilkes played the smaller role of Marc Antony. That being said, that benefit funded the statue of Shakespeare in Central Park that still stands today, so the impact of that performance is quite long lasting.
John Wilkes Booth was famous as an actor, but much of his pre-assassination fame came to him by familial association. If one were to draw a contemporary analogy, John Wilkes Booth was the Stephen Baldwin to Edwin Booth's Alec.
This doesn't entirely answer OP's question, but I hope it's a good start. Perhaps someone with more knowledge of the non-theatrical parts of John Wilkes Booth's life can fill in the cracks about the nation's response to the Lincoln assassination.