This is an odd sentence. Not a sentence that a native speaker would use.

It makes no sense. Not ambiguous, but basically meaningless. . I would like to have been born a boy. <-- Maybe I would like to have a son. <-- maybe . If you beliveve in reincarnation, then, maybe, then it sort of makes sense as "I would like to be reborn a boy."

This is a very old way of saying "I want to give birth to a baby boy." We don't say it that way anymore

In my point of view, that sentence is being said by a female that wanted to be born a male. What is your interpretation of it and why did you find it ambiguous?

As the other native speakers have correctly said, it doesn't make sense. You can find all sorts of rubbish on the internet. Just because someone wrote it, doesn't mean it has a meaning. Trying to interpret something meaningless is futile.