diff --git a/test/scripts/e2e-kind.sh b/test/scripts/e2e-kind.sh
index d355d3a7f1..f145740b73 100755
--- a/test/scripts/e2e-kind.sh
+++ b/test/scripts/e2e-kind.sh
@@ -104,6 +104,13 @@ DUALSTACK_CONVERSION_TESTS="
 should function for service endpoints using hostNetwork
 "
 
+# Skips when default pod network is advertised through BGP
+RA_SKIPPED_TESTS="
+# Pod to ETP local nodeport on a different node is broken
+# https://github.com/ovn-org/ovn-kubernetes/issues/4804
+\[sig-network\] Services should fallback to local terminating endpoints when there are no ready endpoints with externalTrafficPolicy=Local
+"
+
 # Github CI doesn´t offer IPv6 connectivity, so always skip IPv6 only tests.
 #  See: https://github.com/ovn-org/ovn-kubernetes/issues/1522
 SKIPPED_TESTS=$SKIPPED_TESTS$IPV6_ONLY_TESTS
@@ -129,6 +136,11 @@ if [ "$DUALSTACK_CONVERSION" == true ]; then
   SKIPPED_TESTS=$SKIPPED_TESTS$DUALSTACK_CONVERSION_TESTS
 fi
 
+# Skip tests that are unsupported or broken when the default pod network is advertised
+if [ "$ADVERTISE_DEFAULT_NETWORK" == true ]; then
+  SKIPPED_TESTS=$SKIPPED_TESTS$RA_SKIPPED_TESTS
+fi
+
 SKIPPED_TESTS="$(groomTestList "${SKIPPED_TESTS}")"
 
 # if we set PARALLEL=true, skip serial test