Are the Amish living in a modern version of the Middle Ages? Short answer, No.
The Amish are living in twenty-first-century America, just a somewhat different version than most Americans. But they would not be able to live as they do if not surrounded by the modern, commercial US.
Let's start with a few obvious differences between modern Amish life and medieval life. The Amish are now found exclusively in the New World, mostly North America, not Europe. And their religion is a version of Protestantism, not Catholicism. They reject violence, which medieval Christianity was able to deal with at least in some circumstances, and they baptize adults, not infants, as did both medieval and most modern Christians. During the sixteenth-century wars of religion, both Catholics and Protestants decided they were heretics and persecuted them mercilessly. No wonder they still try to stay out of the limelight.
It's generally known that the Amish live a consciously simple life, without electricity, without automobiles, without fashionable dress. But where do they get all the things they need for this simple life? From the rest of us.
Well-water is pumped not by an electric pump but by a windmill. Did an Amish man cut down a tree and carefully carve the vanes from wood? No, he ordered a metal windmill. A Rodeway truck brought it to the farm. Amish clothing is homemade. Did an Amish woman spin and weave her own cloth? No, she bought factory-made cloth, often dyed fairly bright colors (suitable for teenage girls) as well as black and navy.
(Fun fact: You can tell an Amish woman and a conservative Mennonite woman apart at once, even though they wear the same overall style of dress, because the Mennonites always wear prints, to distinguish them from the Amish, who never do. The Amish will however use prints in quilts.)
The Amish drive buggies rather than cars, buggies often made in an Amish workshop--but in many cases made of fiberglass. The buggies are essentially nineteenth-century in style, not medieval; there were no buggies in the Middle Ages. And the brakes are modern, and on New Order buggies there's a battery to run the headlights and taillights. The horses who pull the buggies are often retired race horses. Bicycles are fine in many Amish communities, and they buy their bikes the same way the rest of us do. They use money and checking accounts the same as anyone else.
How about food? The Amish certainly grow a lot of their own. But they also buy a lot of groceries, flour and canned goods and cookies and other processed foods unknown in the Middle Ages. And of course they eat all the foods found in the modern world but not in medieval Europe, such as tomatoes and potatoes and chocolate and corn. They can a lot, using techniques developed in the nineteenth century.
How do they access cloth stores and grocery stores? If they live close by, they can drive their buggy. Otherwise, they will hire a driver and a car or van. The Amish won't have a phone in their house, but they may have a phone booth out by the road, for use in emergency or for use in business. Cell phones have been making headway in the Amish community.
Inside their houses, the Amish will have modern plumbing and a modern kitchen. The stove and refrigerator run off propane, rather than electricity or piped-in gas, and the light is Coleman lanterns rather than overhead electric lights, but they aren't cooking on an open fire by candle light.
Now some accuse the Amish of hypocrisy, claiming they aren't as "simple" as they purport to be. But such an accusation is based on a serious misunderstanding. The Amish aren't trying to live in the Middle Ages. They aren't even trying to live in the nineteenth century, though a lot of their farming techniques went out of style a century ago.
Rather, they are trying to follow a lifestyle that is humble rather than showy and is focused on home and family. The problem with electricity for them is that if you're on the grid, you are making people work on Sundays to get you your electricity 24/7. Same with the gas lines or the phone. The phone can also disrupt family time, making the home accessible to people far away. The car can get you very far away very quickly, whereas with a buggy you won't ever be far from home, and everyone who sees you knows where you're going.
The Amish prefer farming as a family-centered activity, but they aren't medieval peasants. For one thing, they don't have landlords. They all have a basic education and tend to get newspapers and read a lot. And whereas leaving one's family for life in town was a difficult and wrenching decision for a medieval peasant, Amish youth can and do leave the Amish life and still stay in regular contact--as long as they do so before being baptized.