What sense of equivalence do you have in mind?

The major difference between the two questions is that the first one doesn't make any sense, as it presupposes that "logic" is not part of "mathematics". Or at least that seems to have been the consensus of commenters as to why it ought to be closed.

First, let me say (again): MO moderation is not perfectly uniform. That is a fact of life. That's just how having a community moderated website works, and there is no question of having any other moderation model at the moment. In particular, many questions that it would probably be a consensus decision to close slip off the front page without people getting around to closing them. A question not being closed is not an endorsement of it as an acceptable question.

On the other hand, I don't think this pair of questions show the moderating inconsistency you think it does. I don't think Scott actually pinpointed the problem with the first question; the issue is one of being interesting to research mathematicians (or logicians). The first question is ill-posed (does the questioner really mean without learning those subjects or without studying them in university? Do they mean "can" in the sense of no one preventing them from doing so, or in the sense it being something a person can reasonably expect to do). But for almost all variations, the answer is "well, you can do anything you want; it's a free country," but none of these are illuminating. It's just far too vague of a question for the answer to it to tell anyone anything. A question like "What mathematical background does one need to be a research logician" would at least be sensible question (to which one could answer "none" if one wanted, but I suspect some would disagree).

The second is a sensible question; it's clear what question is asking for, and one learns something by reading the answers, though lots of people might not think it's the sort of question MO is intended for. I certainly wouldn't have objected to closing the second question, but I think you can find much worse examples of moderating inconsistency.

There could be an interesting question asked about the relation between logic as part of philosophy and logic as part of mathematics but this was not the question.
The question as is has little to do with logic and it could be asked about any academic field. Indeed it is possible to learn from books and eventually start publishing without learning at a university but it is a remote possibility and it is not recommended. The question as asked is arbitrary and uninteresting. I do not understand the logic in the comparison to the memorable title question. The main difference as people have noted is that the momorable title question was of interest to research mathematicians (at least to some of them) and the other question is of no interest.