There's a part of this question that I can't answer: namely, the part that concerns that "lay" reality of life on the ground in the medieval period, like whether there was ever "mob justice" against atheists, or something like that. But I can talk about the intellectual scene and give a pretty clear answer. Since the medieval period spans many centuries and many locations, I'll just take your cue and look at the end of the 13th century in France.

If you were an intellectual whose professed religious beliefs did not conform to the norm, as laid out by the authorities, you would be excommunicated. An 'intellectual' in this case refers to a philosopher, theologian, university professor, etc. We want to be sort of capacious here because we could be narrow and say something like 'members of the arts faculty in Paris' (which is true) but this would miss the fact that the need for rules about conformity of belief was sparked by people as far away as Denmark who were interpreted as having professed the "wrong" kind of belief (e.g., Boethius of Dacia).

Specifically, we need to talk about the 13th-century "Condemnations." Three times in 13-century Paris, hundreds of statements/propositions were "condemned" -- this means that if you were caught teaching them, you'd be excommunicated unless you went to the bishop and confessed within seven days (in which case you'd get off with a lighter penalty). There was no death penalty or anything like that.

The Condemnations happened in 1210, 1270, and 1277. The Condemnations of 1277 were the biggest. In each case, the leading figure behind the Condemnation was the Bishop of Paris, and in the cases of 1270 and 1277, it was the same Bishop of Paris, Etienne Tempier.

The motivation for the Condemnation is complicated, but it can be boiled down to this: the Bishop of Paris perceived that the philosophical teachings of Aristotle, a Pagan, and Averroes, a Muslim philosopher with very distinctive views, were being widely circulated among European intellectuals. He noticed that they were especially gaining currency in the arts faculty in Paris, and so he condemns the relevant propositions in the territory over which he has a limited jurisdiction: Paris.

Now, what exactly was condemned? Not atheism. Why? Because nobody was an atheist. Atheism was overwhelmingly unpopular among intellectuals up until extremely recently in humanity's intellectual history. I recently wrote an answer to a question here about atheism in the ancient world (or, rather, the lack of it).

Wherever we look in humanity's history, the vast majority of intellectuals (and in many cases, every intellectual) believed in God. There was just no need to condemn atheism. Certainly we can judge that if atheism had been gaining currency in the 13th century, it would have been condemned too. But philosophers just were not even tempted by atheism until well into the modern period.

So, what was condemned? Well, the Condemnations of 1277 condemned 219 propositions, which is too much for us to consider here. But we can categorize them. The first seven of the philosophical propositions bear on the nature and excellence of philosophy. Propositions 8 through 12 have a bearing on the knowability and nature of God. Propositions 13–15 concern divine knowledge, and 16 through 26 divine omnipotence. Many of the articles, notably 34–61 regard the separate angels. Another interesting group of articles is 67–69. Other interesting themes that are touched in the philosophical articles are the world’s eternity (80 through 89), the unicity of the human intellect and its implications (117 through 133), and human freedom and free will (151 through 166). Among the theological articles, themes that appear are theology as a science (180–186), the doctrine of the Eucharist (196–199), Christian morality (202–205), and human immortality and reward and punishment in the life to come (213–219).

We can list all of the propositions condemned in 1270:

1. "That there is numerically one and the same intellect for all humans".

2. "That the soul separated [from the body] by death cannot suffer from bodily fire".

3. "That God cannot grant immortality and incorruption to a mortal and corruptible thing".

4. "That God does not know singulars" (i.e., individual objects or creatures).

5. "That God does not know things other than Himself".

6. "That human acts are not ruled by the providence of God".

7. "That the world is eternal".

8. "That there was never a first human".

All of these are Aristotelian-Averroist beliefs. Aristotle never had a reason to speak on many of these issues explicitly (especially 2 and 8) because he had never any dealings with an Abrahamic religion that would prompt him to. Some of these would be very implausible to attribute to Aristotle (e.g., 1), but the fact is that Averroes believed he was adequately interpreting Aristotle's views when he taught, say, 1, and so we label them 'Aristotelian-Averroist'.

The 13th century saw an increasing number of philosophers/theologians grapple with how persuasive Aristotle's philosophy was. In many cases, such as, mostly famously, Aquinas, there was not a major scandal (though there were always small scandals at least), because philosophers would readily declare that in the event of any conflict between faith and reason, faith would always win. And in the case of Aquinas in particular, he argued there were never any conflicts (although there were times when philosophy was silent and so couldn't even disagree with faith). The Condemnations were a reaction to times when, at least as far as they were interpreted, philosophers were behaving scandalously and too freely endorsing Aristotelian-Averroist beliefs. Atheism was not included because nobody in antiquity or the medieval period was really convinced that atheism was intellectually worthwhile. In conclusion, though, we can certainly say that non-conforming thinkers were threatened with excommunication.