diff --git a/dvc/ignore.py b/dvc/ignore.py
index d11c43053..c9257e520 100644
--- a/dvc/ignore.py
+++ b/dvc/ignore.py
@@ -244,3 +244,7 @@ class CleanTree(BaseTree):
         if self.exists(path):
             return self.tree.stat(path)
         raise FileNotFoundError
+
+    @property
+    def hash_jobs(self):
+        return self.tree.hash_jobs
diff --git a/dvc/remote/base.py b/dvc/remote/base.py
index 8affd571a..5d26c1f25 100644
--- a/dvc/remote/base.py
+++ b/dvc/remote/base.py
@@ -323,7 +323,8 @@ class BaseRemoteTree:
             self.PARAM_CHECKSUM: self.get_hash(path_info, tree=tree, **kwargs)
         }
 
-    def _calculate_hashes(self, file_infos, tree):
+    @staticmethod
+    def _calculate_hashes(file_infos, tree):
         file_infos = list(file_infos)
         with Tqdm(
             total=len(file_infos),
@@ -331,7 +332,7 @@ class BaseRemoteTree:
             desc="Computing file/dir hashes (only done once)",
         ) as pbar:
             worker = pbar.wrap_fn(tree.get_file_hash)
-            with ThreadPoolExecutor(max_workers=self.hash_jobs) as executor:
+            with ThreadPoolExecutor(max_workers=tree.hash_jobs) as executor:
                 tasks = executor.map(worker, file_infos)
                 hashes = dict(zip(file_infos, tasks))
         return hashes
diff --git a/dvc/repo/tree.py b/dvc/repo/tree.py
index ff7d4e707..175d80f95 100644
--- a/dvc/repo/tree.py
+++ b/dvc/repo/tree.py
@@ -421,3 +421,7 @@ class RepoTree(BaseTree):
                 src = root / fname
                 with self.open(src, mode="rb") as fobj:
                     copy_fobj_to_file(fobj, dest / fname)
+
+    @property
+    def hash_jobs(self):
+        return self.repo.tree.hash_jobs
diff --git a/dvc/scm/git/tree.py b/dvc/scm/git/tree.py
index 99d22a00e..2ea999c66 100644
--- a/dvc/scm/git/tree.py
+++ b/dvc/scm/git/tree.py
@@ -183,3 +183,9 @@ class GitTree(BaseTree):
                 to_ctime(entry.ctime),
             )
         )
+
+    @property
+    def hash_jobs(self):
+        # NOTE: gitpython is not threadsafe. See
+        # https://github.com/iterative/dvc/issues/4079
+        return 1
diff --git a/dvc/scm/tree.py b/dvc/scm/tree.py
index 5061c5fbf..c923cd6be 100644
--- a/dvc/scm/tree.py
+++ b/dvc/scm/tree.py
@@ -1,5 +1,8 @@
 import os
 import stat
+from multiprocessing import cpu_count
+
+from funcy import cached_property
 
 
 class BaseTree:
@@ -83,6 +86,10 @@ class WorkingTree(BaseTree):
     def stat(path):
         return os.stat(path)
 
+    @cached_property
+    def hash_jobs(self):
+        return max(1, min(4, cpu_count() // 2))
+
 
 def is_working_tree(tree):
     return isinstance(tree, WorkingTree) or isinstance(