AutoJSAPI requires one to use Init() (usually [1]) in order to know that using the relevant global is ok. AutoEntryScript doesn't [2], and it has caused some issues every now and then and webidl code even explicitly has checks before calling the constructor.
https://searchfox.org/mozilla-central/rev/be4604e4be8c71b3c1dbff2398a5b05f15411673/dom/bindings/CallbackObject.cpp#255,264,271

[1] https://searchfox.org/mozilla-central/rev/be4604e4be8c71b3c1dbff2398a5b05f15411673/dom/script/ScriptSettings.h#215
[2] https://searchfox.org/mozilla-central/rev/be4604e4be8c71b3c1dbff2398a5b05f15411673/dom/script/AutoEntryScript.h#47,51

Sorry, there was a problem with the detection of inactive users. I'm reverting the change.

Duping this to bug 1027553 in Core :: DOM: Core & HTML which is where https://searchfox.org/mozilla-central/source/dom/script/AutoEntryScript.h is categorized to belong per searchfox per moz.build.