It is easy to view Socrates' execution through the lens of totalitarian control of free speech or the stamping out of heresy, but in most respects these don't really fit the situation. Socrates' execution was not part of a broad campaign to stamp out dangerous ideology, it was very specifically targeted on Socrates and specifically happening at that particular time. As is pointed out in both Plato and Xenophon's Apologies the actual contents of Socrates' thought was in most respects rather incidental to his execution, if not outright contradictory of the charges. It is, for example, very difficult to view his thought as actually atheistic (which is something that could get you in trouble) or as a rejection of morality. Conventional morality had already been challenged by the sophists, and it is somewhat difficult to imagine Socrates as being more threatening than, say, Gorgias. And to top it all off, Socrates himself was seventy at his time of his trial and had been doing his thing for decades before.

Now unfortunately it is very difficult to actually know why Socrates was executed despite its popularity as a story because we don't have a single speech, or even an example of a theoretical speech, against him. All we have are the presentations of the opposing arguments within the two Apologies: Xenophon had little interest in portraying the opposing side sympathetically, and Plato had clearly not yet developed his talent for presenting strong opposing arguments, as the accuser Meletus is quite possibly the worst interlocutor to appear in any dialogue. Most people today therefore focus on the rather damning association that Socrates had built up in his life. Critias, one of leaders of the brutal Thirty Tyrants, was an old associate of Socrates. Alcibiades, who betrayed Athens (twice!), was another old friend (despite Plato's dialogues making clear a pretty significant amount of mutual lust they seemingly never consummated an eramenous/erastes relationship). Perhaps more importantly however, the sorts of people Socrates kept in his circle were the sorts of rich and well born idle young men who were thought of, with justification, as sympathetic to the Thirty Tyrants--a good example would be Xenophon himself, who was both pretty nakedly oligarchic (although also somewhat liberal in a modern sense--he is an interesting guy) and had joined a Persian army as a mercenary a few years before. In short, Socrates as a person was viewed as a threat to the democracy.

So it wasn't really about thought control or stamping out dangerous ideologies. It was about Socrates as an individual.