diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index 649cbae4c831..6e2366c4e0df 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -2006,16 +2006,22 @@ def infer_variance(info: TypeInfo, i: int) -> bool:
         for member in all_non_object_members(info):
             if member in ("__init__", "__new__"):
                 continue
-            node = info[member].node
-            if isinstance(node, Var) and node.type is None:
-                tv.variance = VARIANCE_NOT_READY
-                return False
+
             if isinstance(self_type, TupleType):
                 self_type = mypy.typeops.tuple_fallback(self_type)
-
             flags = get_member_flags(member, self_type)
-            typ = find_member(member, self_type, self_type)
             settable = IS_SETTABLE in flags
+
+            node = info[member].node
+            if isinstance(node, Var):
+                if node.type is None:
+                    tv.variance = VARIANCE_NOT_READY
+                    return False
+                if has_underscore_prefix(member):
+                    # Special case to avoid false positives (and to pass conformance tests)
+                    settable = False
+
+            typ = find_member(member, self_type, self_type)
             if typ:
                 typ2 = expand_type(typ, {tvar.id: object_type})
                 if not is_subtype(typ, typ2):
@@ -2036,6 +2042,10 @@ def infer_variance(info: TypeInfo, i: int) -> bool:
     return True
 
 
+def has_underscore_prefix(name: str) -> bool:
+    return name.startswith("_") and not (name.startswith("__") and name.endswith("__"))
+
+
 def infer_class_variances(info: TypeInfo) -> bool:
     if not info.defn.type_args:
         return True
diff --git a/test-data/unit/check-python312.test b/test-data/unit/check-python312.test
index 0b3055212d20..9dc52d2c07b0 100644
--- a/test-data/unit/check-python312.test
+++ b/test-data/unit/check-python312.test
@@ -342,6 +342,69 @@ class Invariant[T]:
 
 reveal_type(c(a1, a2))  # N: Revealed type is "Never"
 
+[case testPEP695InferVarianceUnderscorePrefix]
+# flags: --enable-incomplete-feature=NewGenericSyntax
+
+class Covariant1[T]:
+    def __init__(self, x: T) -> None:
+        self._x = x
+
+    @property
+    def x(self) -> T:
+        return self._x
+
+co1_1: Covariant1[float] = Covariant1[int](1)
+co1_2: Covariant1[int] = Covariant1[float](1)  # E: Incompatible types in assignment (expression has type "Covariant1[float]", variable has type "Covariant1[int]")
+
+class Covariant2[T]:
+    def __init__(self, x: T) -> None:
+        self.__foo_bar = x
+
+    @property
+    def x(self) -> T:
+        return self.__foo_bar
+
+co2_1: Covariant2[float] = Covariant2[int](1)
+co2_2: Covariant2[int] = Covariant2[float](1)  # E: Incompatible types in assignment (expression has type "Covariant2[float]", variable has type "Covariant2[int]")
+
+class Invariant1[T]:
+    def __init__(self, x: T) -> None:
+        self._x = x
+
+    # Methods behave differently from attributes
+    def _f(self, x: T) -> None: ...
+
+    @property
+    def x(self) -> T:
+        return self._x
+
+inv1_1: Invariant1[float] = Invariant1[int](1)  # E: Incompatible types in assignment (expression has type "Invariant1[int]", variable has type "Invariant1[float]")
+inv1_2: Invariant1[int] = Invariant1[float](1)  # E: Incompatible types in assignment (expression has type "Invariant1[float]", variable has type "Invariant1[int]")
+
+class Invariant2[T]:
+    def __init__(self, x: T) -> None:
+        # Dunders are special
+        self.__x__ = x
+
+    @property
+    def x(self) -> T:
+        return self.__x__
+
+inv2_1: Invariant2[float] = Invariant2[int](1)  # E: Incompatible types in assignment (expression has type "Invariant2[int]", variable has type "Invariant2[float]")
+inv2_2: Invariant2[int] = Invariant2[float](1)  # E: Incompatible types in assignment (expression has type "Invariant2[float]", variable has type "Invariant2[int]")
+
+class Invariant3[T]:
+    def __init__(self, x: T) -> None:
+        self._x = Invariant1(x)
+
+    @property
+    def x(self) -> T:
+        return self._x._x
+
+inv3_1: Invariant3[float] = Invariant3[int](1)  # E: Incompatible types in assignment (expression has type "Invariant3[int]", variable has type "Invariant3[float]")
+inv3_2: Invariant3[int] = Invariant3[float](1)  # E: Incompatible types in assignment (expression has type "Invariant3[float]", variable has type "Invariant3[int]")
+[builtins fixtures/property.pyi]
+
 [case testPEP695InheritInvariant]
 # flags: --enable-incomplete-feature=NewGenericSyntax