diff --git a/dvc/odbmgr.py b/dvc/odbmgr.py
index d17291208..ee3d6d524 100644
--- a/dvc/odbmgr.py
+++ b/dvc/odbmgr.py
@@ -1,8 +1,8 @@
-from dvc.fs import Schemes
+from dvc.fs import GitFileSystem, Schemes
 from dvc_data.db import get_odb
 
 
-def _get_odb(repo, settings):
+def _get_odb(repo, settings, fs=None):
     from dvc.fs import get_cloud_fs
 
     if not settings:
@@ -10,7 +10,8 @@ def _get_odb(repo, settings):
 
     cls, config, fs_path = get_cloud_fs(repo, **settings)
     config["tmp_dir"] = repo.tmp_dir
-    return get_odb(cls(**config), fs_path, state=repo.state, **config)
+    fs = fs or cls(**config)
+    return get_odb(fs, fs_path, state=repo.state, **config)
 
 
 class ODBManager:
@@ -42,7 +43,11 @@ class ODBManager:
                 if opt in config:
                     settings[str(opt)] = config.get(opt)
 
-        odb = _get_odb(repo, settings)
+        kwargs = {}
+        if not isinstance(repo.fs, GitFileSystem):
+            kwargs["fs"] = repo.fs
+
+        odb = _get_odb(repo, settings, **kwargs)
         self._odb["repo"] = odb
         self._odb[Schemes.LOCAL] = odb
 
diff --git a/dvc/output.py b/dvc/output.py
index 8cbf227c2..38b20898e 100644
--- a/dvc/output.py
+++ b/dvc/output.py
@@ -341,9 +341,6 @@ class Output:
         self.remote = remote
 
     def _parse_path(self, fs, fs_path):
-        if fs.protocol != "local":
-            return fs_path
-
         parsed = urlparse(self.def_path)
         if parsed.scheme != "remote":
             # NOTE: we can path either from command line or .dvc file,
@@ -386,9 +383,6 @@ class Output:
 
     @property
     def is_in_repo(self):
-        if self.fs.protocol != "local":
-            return False
-
         if urlparse(self.def_path).scheme == "remote":
             return False