The idea is a natural one to present and to consider, although it is also rather problematic.
In a sense it must be true or at least approachable, if only out of a combination of idealistic altruism and fraternity. After all, there are reasons why we call them all religions despite their wild variety. Generally speaking, they tend to be spontaneous attempts at tending to very real social and existential needs that are pretty much universal.
However, factually, the idea that they are all "one" (or equivalent) can only work once one establishes what counts as a religion - or perhaps as a "true" religion. More critically, it can only work if one dares to declare that many a creed does not count as religions, or deliberately avoids the question, somewhat dishonestly IMO.
As for its origin, it seems clear that for the most part it is a well intentioned consequence of the very history of religious beliefs. For a very long time, arguably ever, religious identity was closely linked to tribal (or national) identity and shared many of its goals and advantages with it, along with a number of very serious drawbacks.
Many a sincere adherent realizes that and decides that such a hurdle must be confronted (a conclusion that I happen to agree with).
It turns out that the Bahai Faith must by necessity and origin put that consideration up and front for its own consideration, even if there is nothing explicitly demanding that in its core scriptures. A few decades later a similar realization came to that elusive entity, "the West", leading to a major component of what is now called New Age thinking. Holistic aesthetics all but demand that the idea be at least stated and seriously considered.
Unfortunately, it is still an ultimately unworkable idea, albeit for more prosaic reasons than those offered by most religions. In a nutshell, many self-declared religions are not so much "false" (a remarkably arbitrary statement in itself) as seriously flawed, sometimes to the point of deliberate disfunction, or even insanity and serious crime. It is understandable that altruistic idealists do not want to accept that, but it is nevertheless very much the truth.
