diff --git a/openapi_core/unmarshalling/schemas/unmarshallers.py b/openapi_core/unmarshalling/schemas/unmarshallers.py
index 39617f51..a8077308 100644
--- a/openapi_core/unmarshalling/schemas/unmarshallers.py
+++ b/openapi_core/unmarshalling/schemas/unmarshallers.py
@@ -273,6 +273,14 @@ def unmarshal(self, value: Any) -> Any:
         schema_format = self.find_format(value)
         if schema_format is None:
             return typed
+        # ignore incompatible formats
+        if not (
+            isinstance(value, str)
+            or
+            # Workaround allows bytes for binary and byte formats
+            (isinstance(value, bytes) and schema_format in ["binary", "byte"])
+        ):
+            return typed
         return self.formats_unmarshaller.unmarshal(schema_format, typed)
 
     def get_type_unmarshaller(
diff --git a/tests/integration/unmarshalling/test_unmarshallers.py b/tests/integration/unmarshalling/test_unmarshallers.py
index 6fa0708d..274fa732 100644
--- a/tests/integration/unmarshalling/test_unmarshallers.py
+++ b/tests/integration/unmarshalling/test_unmarshallers.py
@@ -240,6 +240,30 @@ def test_basic_type_formats(
 
         assert result == unmarshalled
 
+    @pytest.mark.parametrize(
+        "type,format,value",
+        [
+            ("string", "float", "test"),
+            ("string", "double", "test"),
+            ("number", "date", 3),
+            ("number", "date-time", 3),
+            ("number", "uuid", 3),
+        ],
+    )
+    def test_basic_type_formats_ignored(
+        self, unmarshallers_factory, type, format, value
+    ):
+        schema = {
+            "type": type,
+            "format": format,
+        }
+        spec = Spec.from_dict(schema, validator=None)
+        unmarshaller = unmarshallers_factory.create(spec)
+
+        result = unmarshaller.unmarshal(value)
+
+        assert result == value
+
     @pytest.mark.parametrize(
         "type,format,value",
         [
@@ -374,23 +398,17 @@ def test_string_uuid_invalid(self, unmarshallers_factory):
         assert len(exc_info.value.schema_errors) == 1
         assert f"is not a 'uuid'" in exc_info.value.schema_errors[0].message
 
-    @pytest.mark.xfail(
-        reason=(
-            "Formats raise error for other types. "
-            "See https://github.com/python-openapi/openapi-schema-validator/issues/66"
-        )
-    )
     @pytest.mark.parametrize(
         "type,format,value,expected",
         [
             ("string", "float", "test", "test"),
             ("string", "double", "test", "test"),
-            ("string", "byte", "test", "test"),
-            ("integer", "date", "10", 10),
-            ("integer", "date-time", "10", 10),
+            ("integer", "byte", 10, 10),
+            ("integer", "date", 10, 10),
+            ("integer", "date-time", 10, 10),
             ("string", "int32", "test", "test"),
             ("string", "int64", "test", "test"),
-            ("integer", "password", "10", 10),
+            ("integer", "password", 10, 10),
         ],
     )
     def test_formats_ignored(
@@ -1728,7 +1746,8 @@ def test_basic_type_oas30_formats_invalid(
         reason=(
             "OAS 3.0 string type checker allows byte. "
             "See https://github.com/python-openapi/openapi-schema-validator/issues/64"
-        )
+        ),
+        strict=True,
     )
     def test_string_format_binary_invalid(self, unmarshallers_factory):
         schema = {
@@ -1748,7 +1767,8 @@ def test_string_format_binary_invalid(self, unmarshallers_factory):
         reason=(
             "Rraises TypeError not SchemaError. "
             "See ttps://github.com/python-openapi/openapi-schema-validator/issues/65"
-        )
+        ),
+        strict=True,
     )
     @pytest.mark.parametrize(
         "types,value",
@@ -1928,7 +1948,8 @@ def unmarshallers_factory(self):
         reason=(
             "OpenAPI 3.1 schema validator uses OpenAPI 3.0 format checker."
             "See https://github.com/python-openapi/openapi-core/issues/506"
-        )
+        ),
+        strict=True,
     )
     @pytest.mark.parametrize(
         "type,format",
diff --git a/tests/unit/templating/test_paths_finders.py b/tests/unit/templating/test_paths_finders.py
index 17396d1a..e26e70c7 100644
--- a/tests/unit/templating/test_paths_finders.py
+++ b/tests/unit/templating/test_paths_finders.py
@@ -173,7 +173,9 @@ class BaseTestServerNotFound:
     def servers(self):
         return []
 
-    @pytest.mark.xfail(reason="returns default server")
+    @pytest.mark.xfail(
+        reason="returns default server",
+    )
     def test_raises(self, finder):
         method = "get"
         full_url = "http://petstore.swagger.io/resource"
diff --git a/tests/unit/unmarshalling/test_schema_unmarshallers.py b/tests/unit/unmarshalling/test_schema_unmarshallers.py
index c25e9005..9d005e99 100644
--- a/tests/unit/unmarshalling/test_schema_unmarshallers.py
+++ b/tests/unit/unmarshalling/test_schema_unmarshallers.py
@@ -197,7 +197,8 @@ def custom_format_validator(value):
         reason=(
             "Not registered format raises FormatterNotFoundError"
             "See https://github.com/python-openapi/openapi-core/issues/515"
-        )
+        ),
+        strict=True,
     )
     def test_schema_format_validator_format_invalid(
         self, schema_unmarshaller_factory, unmarshaller_factory