diff --git a/changelog.d/12601.feature b/changelog.d/12601.feature
new file mode 100644
index 000000000..c13360ff3
--- /dev/null
+++ b/changelog.d/12601.feature
@@ -0,0 +1 @@
+Implement MSC3786: Add a default push rule to ignore m.room.server_acl events.
diff --git a/synapse/config/experimental.py b/synapse/config/experimental.py
index abed5e7ed..b20d94968 100644
--- a/synapse/config/experimental.py
+++ b/synapse/config/experimental.py
@@ -81,3 +81,6 @@ class ExperimentalConfig(Config):
 
         # MSC2815 (allow room moderators to view redacted event content)
         self.msc2815_enabled: bool = experimental.get("msc2815_enabled", False)
+
+        # MSC3786 (Add a default push rule to ignore m.room.server_acl events)
+        self.msc3786_enabled: bool = experimental.get("msc3786_enabled", False)
diff --git a/synapse/push/baserules.py b/synapse/push/baserules.py
index f42f605f2..a17b35a60 100644
--- a/synapse/push/baserules.py
+++ b/synapse/push/baserules.py
@@ -277,6 +277,21 @@ BASE_APPEND_OVERRIDE_RULES: List[Dict[str, Any]] = [
         ],
         "actions": ["dont_notify"],
     },
+    # XXX: This is an experimental rule that is only enabled if msc3786_enabled
+    # is enabled, if it is not the rule gets filtered out in _load_rules() in
+    # PushRulesWorkerStore
+    {
+        "rule_id": "global/override/.org.matrix.msc3786.rule.room.server_acl",
+        "conditions": [
+            {
+                "kind": "event_match",
+                "key": "type",
+                "pattern": "m.room.server_acl",
+                "_cache_key": "_room_server_acl",
+            }
+        ],
+        "actions": ["dont_notify"],
+    },
 ]
 
 
diff --git a/synapse/storage/databases/main/push_rule.py b/synapse/storage/databases/main/push_rule.py
index eb85bbd39..4ed913e24 100644
--- a/synapse/storage/databases/main/push_rule.py
+++ b/synapse/storage/databases/main/push_rule.py
@@ -17,6 +17,7 @@ import logging
 from typing import TYPE_CHECKING, Dict, List, Tuple, Union
 
 from synapse.api.errors import StoreError
+from synapse.config.homeserver import ExperimentalConfig
 from synapse.push.baserules import list_with_base_rules
 from synapse.replication.slave.storage._slaved_id_tracker import SlavedIdTracker
 from synapse.storage._base import SQLBaseStore, db_to_json
@@ -42,7 +43,21 @@ if TYPE_CHECKING:
 logger = logging.getLogger(__name__)
 
 
-def _load_rules(rawrules, enabled_map):
+def _is_experimental_rule_enabled(
+    rule_id: str, experimental_config: ExperimentalConfig
+) -> bool:
+    """Used by `_load_rules` to filter out experimental rules when they
+    have not been enabled.
+    """
+    if (
+        rule_id == "global/override/.org.matrix.msc3786.rule.room.server_acl"
+        and not experimental_config.msc3786_enabled
+    ):
+        return False
+    return True
+
+
+def _load_rules(rawrules, enabled_map, experimental_config: ExperimentalConfig):
     ruleslist = []
     for rawrule in rawrules:
         rule = dict(rawrule)
@@ -51,17 +66,26 @@ def _load_rules(rawrules, enabled_map):
         rule["default"] = False
         ruleslist.append(rule)
 
-    # We're going to be mutating this a lot, so do a deep copy
-    rules = list(list_with_base_rules(ruleslist))
+    # We're going to be mutating this a lot, so copy it. We also filter out
+    # any experimental default push rules that aren't enabled.
+    rules = [
+        rule
+        for rule in list_with_base_rules(ruleslist)
+        if _is_experimental_rule_enabled(rule["rule_id"], experimental_config)
+    ]
 
     for i, rule in enumerate(rules):
         rule_id = rule["rule_id"]
-        if rule_id in enabled_map:
-            if rule.get("enabled", True) != bool(enabled_map[rule_id]):
-                # Rules are cached across users.
-                rule = dict(rule)
-                rule["enabled"] = bool(enabled_map[rule_id])
-                rules[i] = rule
+
+        if rule_id not in enabled_map:
+            continue
+        if rule.get("enabled", True) == bool(enabled_map[rule_id]):
+            continue
+
+        # Rules are cached across users.
+        rule = dict(rule)
+        rule["enabled"] = bool(enabled_map[rule_id])
+        rules[i] = rule
 
     return rules
 
@@ -141,7 +165,7 @@ class PushRulesWorkerStore(
 
         enabled_map = await self.get_push_rules_enabled_for_user(user_id)
 
-        return _load_rules(rows, enabled_map)
+        return _load_rules(rows, enabled_map, self.hs.config.experimental)
 
     @cached(max_entries=5000)
     async def get_push_rules_enabled_for_user(self, user_id) -> Dict[str, bool]:
@@ -200,7 +224,9 @@ class PushRulesWorkerStore(
         enabled_map_by_user = await self.bulk_get_push_rules_enabled(user_ids)
 
         for user_id, rules in results.items():
-            results[user_id] = _load_rules(rules, enabled_map_by_user.get(user_id, {}))
+            results[user_id] = _load_rules(
+                rules, enabled_map_by_user.get(user_id, {}), self.hs.config.experimental
+            )
 
         return results