SO you want to time travel? Well, before doing so wander with me a little bit here....

As medievalists one of the thing we are constantly on guard for are suggestions that peoples of the medieval period (which was about 1000 years mind you) were 'dumb' or 'child-like'. So, reductionist comments like you rightly question:

I'd try to teach them about hygiene, but then they'd burn me at the stake lol

are in fact the legacy of some medieval historians of the 18th and 19th centuries. These writers positioned religion against logic, religion against science for powerful ideological reasons, some historians more than others. But a very influential example of this is 19th century historian Andrew Dickson White, founder of Cornell University, who clearly develops this idea in A History of the Warfare of Science with Theology in Christendom (1896). White was founder of Cornell University! This type of history writing, with emphasis on the forward march of scientific progress and political western liberalism is often called Whig history.

For writers like White, it was important to emphasize liberal ideas of the progress of civilization. And because White believed religion stood in opposition to science, and therefore progress, well, the medieval period became a 'dark ages'.

In fact, there is zero evidence of the Catholic Church or general populations opposing science on scientific terms per se in the medieval period. What we do have evidence of is logic, science, academia at times being at the intersection of religious orthodoxy or political issues, heliocentrism and Galileo being a famous example of both Catholic dogma and politics. In the first case, Catholicism's specific rejection of heliocentrism eventually gave way under evidence, in the second Galileo was as much a victim of personal politics as religious persecution.

Misconceptions about Catholic proscriptions against dissection is another common myth, which I wrote about here and may further some understanding. Some Whigs like to point to the charges of heresy against, and excommunication of, Peter Abelard in the 12th century; simply put, although Abelard was a Catholic, he attempted to subject the belief in God and trinitarianism to the new rigours of logic (called 'dialectics' then). Some fairly influential Cistercian monks like Bernard of Clairvaux thought not that Abelard or what he was saying was in essence incorrect, but that the new dialectical approach to the orthodoxy of Catholicism would undermine the very foundations of faith. None of which is to say that the Catholic church, its leaders, and its wardens were necessarily beneficent in their stance to all science, but it is to to say it was complicated by personality and politics intersecting at moments of orthodoxy moreso than strict orthodoxy itself.

It certainly was not anti-intellectualism: the Catholic church - both local and papal - was responsible for the advent and growth of western universities at Oxford, Paris, Bologna, Montpellier, Toulouse. Medieval science reads like a who's who of monks, abbots, bishops.

Now, to be clear witch burnings of significant patterns and breadth occurred in the transition from medieval to early modern periods. We have very few witch burnings in the medieval period, with sorcery itself not becoming a matter of concern until very late in the 14th century - and fully half of these are seen as politically motivated burnings. Through this period heresy was still a far greater concern for the church, and some parts of the populations. Heresy was not the same as sorcery, although public imagination confuses them. Heretics, or those who weren't reconciled to Catholic orthodoxy, were subject to punishments of anathema and excommunication through out the middle ages, although not by programmatic brute force (ie burnings) until the early 12th century. Many cases of accusation of heresy have turned out to have political motivations as well.

So recent historiography, certainly of the last 30 years, has begun to shed the assumptions of science vs religion conflict and to understand witch burnings as being embedded in politico-cultural conflicts and tensions and then taken up as foundation and cover for petty or large interpersonal or intra-community conflicts.

We have no evidence that someone was burned because they introduced science which then was called sorcery which was in turn considered witchcraft.

We have a lot of evidence of people being accused of witchcraft as a foundation or motivation of other crimes, like murder and theft.

If you go back in time, don't be concerned about sharing scientific understanding - be aware of the political relationships you find yourself in.

edit: order words of