You are presenting an oversimplified picture in both cases, and the contrast is definitely not so clear-cut.
First, the christological and other theological controversies were often only part of much broader political, ideological, ethnic, and other conflicts, involving all sorts of parties and factions both within and outside the church hierarchy. Sometimes there was also a strong populist element—during the monophysite controversy, for example, there were plenty of spontaneous riots and pogroms. Therefore, in these controversies, the power and status of many groups and individuals was at stake, not just the interests of the Church leadership.
Second, the modern repercussions of various ideological transgressions are by no means limited to spontaneous reactions by people who feel directly targeted. For start, there is a complicated and non-obvious system that determines which groups are entitled to such reaction, so that their outrage will be supported and the offenders condemned by the respectable opinion, and which groups are OK to denigrate, so that protesting will only lower their status still further. Then, we also have a network of official intellectual institutions that have a de facto monopoly of respectable and impactful thinking, and the reaction of these institutions to various ideological transgressions involves many elements far beyond direct and spontaneous outrage of those who are (supposed to be) directly targeted.
But aside from all this, my main point is the contrast between two kinds of systems that is independent of the issues you raise:
A system in which certain beliefs are clearly spelled out as official dogma that it is forbidden to question, so if you’re accused of heresy, you can at least demand a clear statement of what exact official dogma you have contradicted—and if you have in fact steered clear of any matters of official dogma in your writings and utterances, this is admissible as a valid defense. (Historically, this was typically the case for people accused of heresy by the Church tribunals, though of course things varied a lot in different places and times and there were certainly instances of corruption and railroading, like in any other legal system.)
A system in which there is official pretense that there is no dogma whatsoever, that everyone is supposed to be a skeptical free thinker about everything, and that imposing some sort of official dogma would be the vilest tyranny imaginable—so that when you are accused of some ideological transgression, it is automatically assumed that your statements must be due to either disingenuous malice or some crazy delusion, since the respectable opinion is considered to be a product of pure rational thinking, as an assumption built into the system. So rather than having clearly outlined boundaries of what you may or may not say, you must pretend to be a free thinker unencumbered by any official dogma, while at the same time strictly adhering to the de facto official dogma—which is only more sweeping and onerous because it is so vague and not stated openly.
It seems to me that system (2) is hardly an improvement over (1).
You are presenting an oversimplified picture in both cases, and the contrast is definitely not so clear-cut.
First, the christological and other theological controversies were often only part of much broader political, ideological, ethnic, and other conflicts, involving all sorts of parties and factions both within and outside the church hierarchy. Sometimes there was also a strong populist element—during the monophysite controversy, for example, there were plenty of spontaneous riots and pogroms. Therefore, in these controversies, the power and status of many groups and individuals was at stake, not just the interests of the Church leadership.
Second, the modern repercussions of various ideological transgressions are by no means limited to spontaneous reactions by people who feel directly targeted. For start, there is a complicated and non-obvious system that determines which groups are entitled to such reaction, so that their outrage will be supported and the offenders condemned by the respectable opinion, and which groups are OK to denigrate, so that protesting will only lower their status still further. Then, we also have a network of official intellectual institutions that have a de facto monopoly of respectable and impactful thinking, and the reaction of these institutions to various ideological transgressions involves many elements far beyond direct and spontaneous outrage of those who are (supposed to be) directly targeted.
But aside from all this, my main point is the contrast between two kinds of systems that is independent of the issues you raise:
A system in which certain beliefs are clearly spelled out as official dogma that it is forbidden to question, so if you’re accused of heresy, you can at least demand a clear statement of what exact official dogma you have contradicted—and if you have in fact steered clear of any matters of official dogma in your writings and utterances, this is admissible as a valid defense. (Historically, this was typically the case for people accused of heresy by the Church tribunals, though of course things varied a lot in different places and times and there were certainly instances of corruption and railroading, like in any other legal system.)
A system in which there is official pretense that there is no dogma whatsoever, that everyone is supposed to be a skeptical free thinker about everything, and that imposing some sort of official dogma would be the vilest tyranny imaginable—so that when you are accused of some ideological transgression, it is automatically assumed that your statements must be due to either disingenuous malice or some crazy delusion, since the respectable opinion is considered to be a product of pure rational thinking, as an assumption built into the system. So rather than having clearly outlined boundaries of what you may or may not say, you must pretend to be a free thinker unencumbered by any official dogma, while at the same time strictly adhering to the de facto official dogma—which is only more sweeping and onerous because it is so vague and not stated openly.
It seems to me that system (2) is hardly an improvement over (1).