diff --git a/e2e/scripts/st_file_uploader.py b/e2e/scripts/st_file_uploader.py
index 1ecc534993b3..5475d1e2d496 100644
--- a/e2e/scripts/st_file_uploader.py
+++ b/e2e/scripts/st_file_uploader.py
@@ -20,6 +20,10 @@
 else:
     st.text(single_file.read())
 
+# Here and throughout this file, we use if st._is_running_with_streamlit:
+# since we also run e2e python files in "bare Python mode" as part of our
+# Python tests, and this doesn't work in that circumstance
+# st.session_state can only be accessed while running with streamlit
 if st._is_running_with_streamlit:
     st.write(repr(st.session_state.single) == repr(single_file))
 
@@ -56,3 +60,20 @@
         st.text("No upload")
     else:
         st.text(form_file.read())
+
+
+if st._is_running_with_streamlit:
+    if not st.session_state.get("counter"):
+        st.session_state["counter"] = 0
+
+    def file_uploader_on_change():
+        st.session_state.counter += 1
+
+    st.file_uploader(
+        "Drop a file:",
+        type=["txt"],
+        key="on_change_file_uploader_key",
+        on_change=file_uploader_on_change,
+    )
+
+    st.text(st.session_state.counter)
diff --git a/e2e/specs/st_file_uploader.spec.js b/e2e/specs/st_file_uploader.spec.js
index 9194efc665ad..3bd0f7410baa 100644
--- a/e2e/specs/st_file_uploader.spec.js
+++ b/e2e/specs/st_file_uploader.spec.js
@@ -393,4 +393,51 @@ describe("st.file_uploader", () => {
       );
     });
   });
+
+  // regression test for https://github.com/streamlit/streamlit/issues/4256 bug
+  it("does not call a callback when not changed", () => {
+    const fileName1 = "file1.txt";
+    const uploaderIndex = 4;
+
+    cy.fixture(fileName1).then(file1 => {
+      const files = [
+        { fileContent: file1, fileName: fileName1, mimeType: "text/plain" }
+      ];
+
+      // Script contains counter variable stored in session_state with
+      // default value 0. We increment counter inside file_uploader callback
+      // Since callback did not called at this moment, counter value should
+      // be equal 0
+      cy.getIndexed("[data-testid='stText']", uploaderIndex).should(
+        "contain.text",
+        "0"
+      );
+
+      // Uploading file, should invoke on_change call and counter increment
+      cy.getIndexed(
+        "[data-testid='stFileUploadDropzone']",
+        uploaderIndex
+      ).attachFile(files[0], {
+        force: true,
+        subjectType: "drag-n-drop",
+        events: ["dragenter", "drop"]
+      });
+
+      // Make sure callback called
+      cy.getIndexed("[data-testid='stText']", uploaderIndex).should(
+        "contain.text",
+        "1"
+      );
+
+      // On rerun, make sure callback is not called, since file not changed
+      cy.get("body").type("r");
+      cy.wait(1000);
+
+      // Counter should be still equal 1
+      cy.getIndexed("[data-testid='stText']", uploaderIndex).should(
+        "contain.text",
+        "1"
+      );
+    });
+  });
 });
diff --git a/scripts/run_bare_integration_tests.py b/scripts/run_bare_integration_tests.py
index 1123670b7e87..67bcb71cc59b 100755
--- a/scripts/run_bare_integration_tests.py
+++ b/scripts/run_bare_integration_tests.py
@@ -29,9 +29,6 @@
 from typing import Set
 
 import click
-import matplotlib
-
-IS_PYTHON_3_6 = sys.version_info[:2] == (3, 6)
 
 # Where we expect to find the example files.
 E2E_DIR = "e2e/scripts"
@@ -47,10 +44,6 @@
 # that doesn't require a display.
 os.environ["MPLBACKEND"] = "Agg"
 
-# magic.py uses contextlib.asynccontextmanager, which is Python 3.7+
-if IS_PYTHON_3_6:
-    EXCLUDED_FILENAMES.add("st_magic.py")
-
 
 def _command_to_string(command):
     if isinstance(command, list):