Correctly set -stdlib=libc++ when building with a custom libc++.

build/config/sanitizers/BUILD.gn

 # Copyright 2014 The Chromium Authors. All rights reserved.
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
 import("//build/config/chrome_build.gni")
 import("//build/config/chromecast_build.gni")
 import("//build/config/sanitizers/sanitizers.gni")
 import("//build/toolchain/toolchain.gni")
 
 # Contains the dependencies needed for sanitizers to link into executables and
 # shared_libraries. Unconditionally depend upon this target as it is empty if
 # |is_asan|, |is_lsan|, |is_tsan|, |is_msan| and |use_custom_libcxx| are false.
 group("deps") {
-  deps = [
+  public_deps = [
     ":deps_no_options",
   ]
   if (using_sanitizer) {
     public_configs = [
       ":sanitizer_options_link_helper",
 
       # Even when a target removes default_sanitizer_flags, it may be depending
       # on a library that did not remove default_sanitizer_flags. Thus, we need
       # to add the ldflags here as well as in default_sanitizer_flags.
       ":default_sanitizer_ldflags",
     ]
-    deps += [ ":options_sources" ]
+    deps = [
+      ":options_sources",
+    ]
   }
 }
 
 group("deps_no_options") {
   if (using_sanitizer) {
     public_configs = [
       # Even when a target removes default_sanitizer_flags, it may be depending
       # on a library that did not remove default_sanitizer_flags. Thus, we need
       # to add the ldflags here as well as in default_sanitizer_flags.
       ":default_sanitizer_ldflags",
     ]
     deps = []
     if (use_prebuilt_instrumented_libraries) {
       deps += [ "//third_party/instrumented_libraries:deps" ]
     }
     if (use_custom_libcxx) {
-      deps += [ "//buildtools/third_party/libc++:libcxx_proxy" ]
+      public_deps = [
+        "//buildtools/third_party/libc++:libcxx_proxy",
+      ]
     }
     if (is_mac) {
       data_deps = [
         ":copy_asan_runtime",
       ]
     }
   }
 }
 
 if (is_mac) {
@@ skipping 345 matching lines @@
 # This allows to selectively disable ubsan_vptr, when needed. In particular,
 # if some third_party code is required to be compiled without rtti, which
 # is a requirement for ubsan_vptr.
 config("default_sanitizer_flags_but_ubsan_vptr") {
   configs = all_sanitizer_configs - [ ":ubsan_vptr_flags" ]
 }
 
 config("default_sanitizer_flags_but_coverage") {
   configs = all_sanitizer_configs - [ ":coverage_flags" ]
 }