Jews maybe, occasionally, although the most notorious of Jewish persecutions by (sort of) Church authorities, the Spanish Inquisition, was really about Jews who had ostensibly converted to Christianity but were suspected of still observing Jewish laws and rituals in private. Thus, from the Church’s point of view, this was about heretical or apostate Christians.
As for atheists, in another recent thread I put out a general challenge to come up with a single instance of anyone persecuted for atheism (in anything like the modern sense of that term: believing that there are no gods) in ancient or medieval times, either by Christian authorities or the authorities of any other religion. This was after another poster had asserted that atheists throughout history had routinely been persecuted and murdered by the religious for their (lack of) belief. Nobody could come up with any examples earlier than that of Percy Shelly, who was expelled from Oxford (not murdered) ostensibly for being an atheist (really, of course, making a lot of noise about it and related political issues) in the early 19th century.
This is mainly, of course, because there were no fricking unbelievers to be persecuted during the middle ages. The social and intellectual conditions conducive to atheism did not exist. A few atheists (or quasi-atheists) did, arguably, exist in the ancient, pre-Christian era. The Epicureans are fairly reasonably construed as atheists, although they did not quite deny that gods existed, just that they mattered. However, I know of no evidence that Epicureans as such (or any other “ancient atheists” that may conceivably have existed) ever suffered persecution from the religious institutions of the religious majority around them.
Anyway, I am in no way arguing that the Church, when it had the relevant power, was “incredibly tolerant” of religious dissent. It most certainly was not, and often persecuted those suspected of heresy very harshly indeed. However, to describe this in the way the OP did as a matter of being routinely “oppressive toward non-believers” is thoroughly misleading, suggesting the nonsensical myth of atheists having been martyred for their unbelief down through the ages.
Heretics, the people who actually did get oppressed by Church authorities for many centuries, were not non-believers, they were Christian believers, often fanatical believers, who believed in some variant form of Christianity that Church leaders thought (rightly or wrongly) to be dangerous to Christian solidarity (and thus the leadership’s grip on power). Most often these heretics were considerably more fanatical and inflexible in their religious belief than the Church leaders were. Jews, being non-evangelizers, were not much of a threat to that power, which is why most of the persecutions of Jews in the middle ages were not orchestrated (though not necessarily opposed either) by Church authorities. Atheists were not a threat because they didn’t exist. Heretics - people promoting variant versions of Christianity - really were a serious threat to Church power, as was eventually proved when all efforts to suppress one of them (Martin Luther) failed.
