Before one more person comes here to say "water":
Medieval people drank water. Coroners' reports from 14th century England tell of young children who drowned when they fell into creeks while trying to scoop water into a cup to drink. "Bread and water" was the standard penitential and perpetual-imprisonment diet. &c.
Watered-down (watered-down) wine, ale, and beer were popular drinks for socio-economic and taste reasons, not because water was inherently unsafe. Water was the "beggars' drink" because it was free. Drinking ale meant you could afford to drink ale/afford the time to make it for yourselves.
Medieval people understood that some water was dirty. In Viterbo, a giant riot that resulted in the death of a local woman exploded after a visiting cardinal's assistant bathed his puppy in the local fountain from which drinking water was drawn.
Medieval people understood that boiling dirty water could help. A 14th century letter from a man to his sons at university in Toulouse reminds them that one of the local rivers has dirty water, and they must not drink it unless they "cook" it.
Oh! I completely forgot earlier: I've previously discussed the difference between diets in England, ca. 1500, and modern America, if anyone is interested!
Just to make sure I understand your question appropriately -- you want to know that if you traveled to medieval Europe, given that your gut microbiome (and body in general) has acclimated to a 21st century that has modern food preservation and supply chains, would there be bacteria so alien that your body wouldn't be able to handle it?
Let let's take this question very seriously. Caveat number one -- most of my knowledge on food safety comes from physician AWARENESS of food safety. Because of this, I can't really comment of the 13th century. Medical knowledge of food was colored by our knowledge of the four humors and spoiling food would have been seen as either a part of pepsis (the healthy breakdown of food into the constituent humors; thought to occur with digestion), or sepsis (the unhealthy breakdown of food associated with disease; also associated with swamps, foul odors -- but all abiogenesis, the association with new life). There was not a clear understanding that the spoiling of food was a separate process than what happened inside the human body. In fact, the modern (early to middle 19C) debate on digestion is super interesting and pretty much led to our understanding of organic chemistry, but I'll temper my excitement.
So what would happen if a modern microbiome were exposed to the 13th century CE? First of all, I'm assuming that prevalence patterns are similar to today (that's an unfair assumption since the Colombian exchange had not yet happened, and there didn't yet exist the selective pressures of antibiotics). But I think it's fair to say that you would get an acute gastroenteritis. Like, a bad one, within 1-3 weeks. And the odds of this happening would be very high (up to 60%). The most common organism would likely be ETEC (that's toxigenic e. coli), but also campylobacter, Shigella spp, Salmonella species, and all sorts of viruses. Adding to that, parasititic infections of water sources were common, so I'd expect giardia, crypto, and entameoba histolytica to cause quite a problem as well. This is where your location likely matters -- by the 18th and 19th century, these infections were endemic in cities prior to modern sanitation, but a rural area in the thirteenth century likely would have a lower risk of parasitic species that require a human host.
Assuming you survived (reasonably likely), your gut would likely quickly advance. There's been a lot of exciting research into the adaptability of the gut microbiome in the last decade, and it appears that the bacteria in your gut can change rapidly -- like over the course of weeks -- to provide protection (a popular science article is here: https://www.scientificamerican.com/article/the-guts-microbiome-changes-diet/). That's why, when I worked in Botswana and American residents rotated with me, they would often get travelers diarrhea, but me and my wife were fine.
OK -- so are there foods that non-moderns would have recognized as being unsafe to eat, even for themselves? And the answer is, of course. u/Sunagainstgold points out contemporaneous examples in which people avoided obviously spoiled food and spoiled water. And the way the Hippocratic corpus and Galen describe it, it's OBVIOUS that people would avoid spoiled food (what they are interested in is WHY spoiled food causes disease, as above).
I can't really answer for the 13C, so let's talk about England in the 18th and 19th C, when the first modern (though pre-germ theory) understandings of food-born illness start to come into focus. It was generally understood that in the summer, consumption of meat products, even if the meat was not obviously spoiled, was associated with "cholera" (not the blue or asiatic cholera; basically the syndrome we're describing above, that of an acute gastroenteritis). Generic advice was to avoid meat in these times. And there was also an increasing understanding about the danger of contaminated drinking water. u/Valmyr5 has a good response below about Snow and the Broad Street pump -- and there were other pumps with filthy, smelly water that Snow first fingered. That wasn't controversial in mid 19th century London, though. The idea that foul smells could cause disease (miasma) was ascendant, with the contagion theory of disease still hotly debated. The Broad Street pump, in fact, was renowned for its sweet, drinkable water, which is the major reason Snow was not believed. And I should point out that the Board of Health was actually against Snow, and officially determined the outbreak was due to miasma -- it was Snow and his friend Henry Whitehead's personal testimony to the local board of guardians that got the pump handle removed (by the way, The Ghost Map is one of the best books about population health I've ever read, and is all about Snow and Whitehead's investigations -- https://www.amazon.com/Ghost-Map-Londons-Terrifying-Epidemic/dp/1594482691).
Okay, that was a little bit rambly. The TL;DR: if you go back to the 13th century and start to eat the food, you will get an immediate gastroenteritis. If you survive this (and the odds are pretty good), your gut will pretty much adapt to many of the organisms. However, there will still be foods (and contaminated water) that would cause you problems, especially meat in the summer. The idea of spoiled food would be widespread, though.