diff --git a/conda_build/metadata.py b/conda_build/metadata.py
index 5cc5bc129a..2b8443e68c 100644
--- a/conda_build/metadata.py
+++ b/conda_build/metadata.py
@@ -1597,21 +1597,34 @@ def ms_depends(self, typ="run"):
             try:
                 ms = MatchSpec(spec)
             except AssertionError:
-                raise RuntimeError(f"Invalid package specification: {spec!r}")
+                if len(self.undefined_jinja_vars) == 0:
+                    raise RuntimeError(f"Invalid package specification: {spec!r}")
+                else:
+                    continue
             except (AttributeError, ValueError) as e:
-                raise RuntimeError(
-                    "Received dictionary as spec.  Note that pip requirements are "
-                    "not supported in conda-build meta.yaml.  Error message: " + str(e)
-                )
+                if len(self.undefined_jinja_vars) == 0:
+                    raise RuntimeError(
+                        "Received dictionary as spec.  Note that pip requirements are "
+                        "not supported in conda-build meta.yaml.  Error message: "
+                        + str(e)
+                    )
+                else:
+                    continue
+
             if ms.name == self.name() and not (
                 typ == "build" and self.config.host_subdir != self.config.build_subdir
             ):
                 raise RuntimeError(f"{self.name()} cannot depend on itself")
+
+            # TODO: IDK what this does since AFAIK the inner continue applies only
+            # to the inner loop
             for name, ver in name_ver_list:
                 if ms.name == name:
                     if self.noarch:
                         continue
 
+            # TODO: the validation here appears to be a waste of time since MatchSpec
+            # appears to validate?
             for c in "=!@#$%^&*:;\"'\\|<>?/":
                 if c in ms.name:
                     sys.exit(
diff --git a/news/5555-skip-bad-specs-while-still-parsing.rst b/news/5555-skip-bad-specs-while-still-parsing.rst
new file mode 100644
index 0000000000..1454fb9bad
--- /dev/null
+++ b/news/5555-skip-bad-specs-while-still-parsing.rst
@@ -0,0 +1,19 @@
+### Enhancements
+
+* <news item>
+
+### Bug fixes
+
+* Fixed a bug where bad match specs from intermediate parsing results would cause parsing to fail. (#5555)
+
+### Deprecations
+
+* <news item>
+
+### Docs
+
+* <news item>
+
+### Other
+
+* <news item>
diff --git a/tests/test_api_build.py b/tests/test_api_build.py
index d6a519cc5a..3e70dd64fe 100644
--- a/tests/test_api_build.py
+++ b/tests/test_api_build.py
@@ -2082,7 +2082,7 @@ def test_conda_build_script_errors_without_conda_info_handlers(tmp_path, recipe,
 
 def test_api_build_inject_jinja2_vars_on_first_pass(testing_config):
     recipe_dir = os.path.join(metadata_dir, "_inject_jinja2_vars_on_first_pass")
-    with pytest.raises(RuntimeError):
+    with pytest.raises((RuntimeError, CondaBuildUserError)):
         api.build(recipe_dir, config=testing_config)
 
     testing_config.variant = {"python_min": "3.12"}
diff --git a/tests/test_metadata.py b/tests/test_metadata.py
index d5feecf53c..3985bdc1df 100644
--- a/tests/test_metadata.py
+++ b/tests/test_metadata.py
@@ -655,3 +655,56 @@ def test_parse_until_resolved_skip_avoids_undefined_jinja(
         pytest.fail(
             "Undefined variable caused error, even though this build is skipped"
         )
+
+
+@pytest.mark.parametrize("have_variant", [True, False])
+def test_parse_until_resolved_missing_jinja_in_spec(
+    testing_metadata: MetaData,
+    tmp_path: Path,
+    have_variant: bool,
+) -> None:
+    (recipe := tmp_path / (name := "meta.yaml")).write_text(
+        """
+package:
+    name: dummy
+    version: 1.0.0
+
+build:
+    noarch: python
+    number: 0
+
+requirements:
+    host:
+        - python ={{ python_min }}
+    run:
+        - python >={{ python_min }}
+"""
+    )
+    (tmp_path / "conda_build_config.yaml").write_text(
+        """
+python_min:
+    - 3.6
+"""
+    )
+    testing_metadata._meta_path = recipe
+    testing_metadata._meta_name = name
+    if have_variant:
+        testing_metadata.config.variant = {"python_min": "3.6"}
+    else:
+        delattr(testing_metadata.config, "variant")
+        delattr(testing_metadata.config, "variant_config_files")
+        delattr(testing_metadata.config, "variants")
+
+    try:
+        testing_metadata.parse_until_resolved()
+        if not have_variant:
+            pytest.fail("Undefined variable did NOT cause spec parsing error!")
+        else:
+            print("parsed OK!")
+    except (Exception, SystemExit):
+        if have_variant:
+            pytest.fail(
+                "Undefined variable caused spec parsing error even if we have the variant!"
+            )
+        else:
+            print("did not parse OK!")