You should completely remove "This answer is Googleable" from your vocabulary because it is a gross mis-characterization of the issue.
We've experimented with a close reason called general reference to rid some sites of ultra-basic questions — questions that are asked in such a lazy fashion as to be easily findable in references designed to quickly and effortlessly find that information. For example:
Question: What is the Qur'an?
Answer: "Grrr... Why don't you just look it up?!"
closed as [general reference]
This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information.
But we have all-but-given up adding this close-reason across the network precisely because of this kind of misunderstanding. People are quick to conflate the problems of "general reference" questions with "anything that is easily googleable"… and the close hammer starts coming down without thought or understanding behind the prohibition.
There are questions which are simply too trivial to ask. It's not about being too easy or easily googlable… It's about boring to tears the very users you are trying to attract. There's nothing wrong with an intriguing easy question asked with care and forethought of purpose, but you have to stay keenly focused on asking questions as you would ask them to an "expert."
To attract experts, you need people asking interesting and challenging questions. A site where experts are answering your questions will attract a broader audience. But experts will NOT use a site that starts out top-heavy with trite "busy work."
Personally, I would vote that they should be allowed. Googling for answers on Islam has varying degrees of success (depending on the question). There are far too many single sided articles out there. One of the reasons (I believe) for the existence of this SE site is to allow for multiple viewpoints and answers.
Googling may give you an answer, but it may not be a correct answer. With topics other than Islam, there's often enough of a problem with inadvertent misinformation. With Islam, the situation is worse, because there's the potential problem of deliberate misinformation.