Remove direct uses of TestingFunctionFactory

Replace them with uses of TestingFactory which is based
on base::Callback<> instead of function pointers.

This converts uses in /chrome/browser/sync.

This CL was uploaded by git cl split.

R=tschumann@chromium.org

Bug: 809610
Change-Id: If489e869a7f9143528ef89411b1a8d7c6e24b79b
Reviewed-on: https://chromium-review.googlesource.com/c/1245729Reviewed-by: Mikel Astiz <mastiz@chromium.org>
Commit-Queue: Sylvain Defresne <sdefresne@chromium.org>
Cr-Commit-Position: refs/heads/master@{#596227}

chrome/browser/sync/test/integration/sync_test.cc

@@ -693,19 +693,20 @@ void SyncTest::SetUpInvalidations(int index) {
     }
     case SERVER_TYPE_UNDECIDED:
     case LOCAL_PYTHON_SERVER:
-      BrowserContextKeyedServiceFactory::TestingFactoryFunction
-          invalidation_provider =
+      BrowserContextKeyedServiceFactory::TestingFactory invalidation_provider =
+          base::BindRepeating(
               TestUsesSelfNotifications()
-                  ? BuildSelfNotifyingP2PProfileInvalidationProvider
-                  : BuildRealisticP2PProfileInvalidationProvider;
+                  ? &BuildSelfNotifyingP2PProfileInvalidationProvider
+                  : &BuildRealisticP2PProfileInvalidationProvider);
       if (fcm_invalidations_enabled) {
         invalidation::ProfileInvalidationProviderFactory::GetInstance()
-            ->SetTestingFactoryAndUse(GetProfile(index), invalidation_provider);
+            ->SetTestingFactoryAndUse(GetProfile(index),
+                                      std::move(invalidation_provider));
       } else {
         invalidation::DeprecatedProfileInvalidationProviderFactory::
             GetInstance()
                 ->SetTestingFactoryAndUse(GetProfile(index),
-                                          invalidation_provider);
+                                          std::move(invalidation_provider));
       }
   }
 }