The notion of "free speech", as we understand it today did not exist in the Roman empire.
The authors you cite probably mean " crimen laesae majestatis", which English Wikipedia
translates as "lese majeste". This was a law which was probably introduced under Augustus,
and then revoked and re-introduced under various princepces. The first person who revoked it
was Vespasian, if I remember correctly. It was not enforced under Marcus, and probably under
his predecessors (Trajan, Hadrian, Antonine ...).
So you could say anything about the princeps (or even about his family) during the rule of these liberal princepces. Even in public performances.
Persecution of Christians is a very different matter. There was an established State religion,
and established rituals. Refusal to perform them or to participate in them was considered a political act, kind of rejection of the Empire itself. It is not the personal beliefs or speech which was persecuted in this case.
But a kind of denial of the supreme authority of the empire.
The laws against Christians were not always strictly enforced (or even enforced at all).
A very typical is the attitude of Pliny the younger, who was a governor of a province under Trajan. He did not search for Christians. But those denounced he had to interrogate.
If they persisted and refused to perform certain symbolic rituals for established gods, they were executed. (After a third warning and third refusal).
Pliny himself says (in a letter to Trajan) that this weird superstition is harmless by itself. But a stubborn denial of the authority and of the established rites deserves
a death sentence.
Edit. Interestingly, Dante places Trajan in Paradise, though the proper place for "righteous pagans" according to the official doctrine was the Purgatory. Anyway, Trajan was the only Roman emperor considered a righteous pagan, apparently they do not blame him with his moderate persecution of Christians.