diff --git a/compiler/rustc_const_eval/src/check_consts/check.rs b/compiler/rustc_const_eval/src/check_consts/check.rs
index 4110317adcf4..66a2afa0aa7d 100644
--- a/compiler/rustc_const_eval/src/check_consts/check.rs
+++ b/compiler/rustc_const_eval/src/check_consts/check.rs
@@ -853,9 +853,7 @@ impl<'tcx> Visitor<'tcx> for Checker<'_, 'tcx> {
                 }
 
                 // Intrinsics are language primitives, not regular calls, so treat them separately.
-                if let Some(intrinsic) = tcx.intrinsic(callee)
-                    && intrinsic.name != sym::offset_of
-                {
+                if let Some(intrinsic) = tcx.intrinsic(callee) {
                     if !tcx.is_const_fn(callee) {
                         // Non-const intrinsic.
                         self.check_op(ops::IntrinsicNonConst { name: intrinsic.name });
@@ -888,6 +886,15 @@ impl<'tcx> Visitor<'tcx> for Checker<'_, 'tcx> {
                             feature,
                             ..
                         }) => {
+                            // We only honor `span.allows_unstable` aka `#[allow_internal_unstable]`
+                            // if the callee is safe to expose, to avoid bypassing recursive stability.
+                            // This is not ideal since it means the user sees an error, not the macro
+                            // author, but that's also the case if one forgets to set
+                            // `#[allow_internal_unstable]` in the first place.
+                            if self.span.allows_unstable(feature) && is_const_stable {
+                                return;
+                            }
+
                             self.check_op(ops::IntrinsicUnstable {
                                 name: intrinsic.name,
                                 feature,
diff --git a/library/core/src/intrinsics/mod.rs b/library/core/src/intrinsics/mod.rs
index 18d8b9880dfa..374c749c2da0 100644
--- a/library/core/src/intrinsics/mod.rs
+++ b/library/core/src/intrinsics/mod.rs
@@ -2802,7 +2802,6 @@ pub const fn align_of<T>() -> usize;
 #[rustc_nounwind]
 #[unstable(feature = "core_intrinsics", issue = "none")]
 #[rustc_const_unstable(feature = "core_intrinsics", issue = "none")]
-#[rustc_const_stable_indirect]
 #[rustc_intrinsic_const_stable_indirect]
 #[rustc_intrinsic]
 #[lang = "offset_of"]