I think, actually, the problem is framed backwards.
The statement,"all religions are the same" assumes that first something definable exists which is, by itself, "religion"
and then only after establishing that assumption, says "this is religion, that is not religion" and so forth, and then "because these two things share an outward appearance, and one of them is 'religion' then both of them are 'religion' and therefore the same".
But what is "religion?" if we say that it is a search for peace of mind, or for happiness, then all sorts of things can be called 'religion'. Everything we do, going to a job, going to war, from the Buddhist understanding, is ultimately a quest for happiness and peace of mind. Most paths don't get us there, but the goal is the same. So, politics becomes 'religion'. Health care becomes 'religion' and so forth.
If we say that it is a journey of the soul or the spirit or whatever, then you have to define all those terms.
If 'religion' is rules and rituals, then again, any set of rules is 'religion'. Putting candles on a cake is a birthday ritual. But most people would not call that 'religion' even though candles and birth observances are often associated with 'religion'.
Then, you have to ask, "why do you call Buddhism a 'religion'? Is it because books on Buddhism are usually found in the 'religion' section of the bookstore or library? Is it because we have always heard "Buddhism: one of the world's great religions"? Buddhism doesn't assert the existence of a God, or of sins, or anything like that. Somebody may have called it a 'religion' but whoever that was, it wasn't the Buddha.
What The Buddha realized that despite people having religion or not, regardless of what people believed, whether they thought about gods or sacred rivers or demons or whatever, everyone was always striving for peace of mind, to be free from suffering and the causes of suffering, and to have happiness and the causes of happiness. If a person followed a religion or not, was to him really beside the point.
For that reason, Buddhism is not is competition with religion, and does not need to be put into the category of religion. You could certainly put it into the same category as "institutions in which people wear robes and chant with beads" but then again you could just as easily put it into the same category as "institutions which construct large and elaborate buildings" along with hospitals and automobile companies. But all these identifiers would really be irrelevant.
It is important not to confuse the teachings (Dharma) with the institutions which have preserved the teachings over so many centuries. You could say that the Dharma teachings have been preserved in institutions which to the western observer greatly resemble the religious institutions that arose in Europe. We use words such as "holy" and "sacred" and maybe even "prayer", but these are English language words used as simple translations for a variety of concepts.
Making such comparisons only happens if you already have some concept of a western church to compare it to. If you had never seen a Catholic monk praying with a rosary, it would never occur to you that a Buddhist monk with a mala looks similar.
So, a person may follow a religion or be an atheist, and still practice meditation, compassion, and many of the other things that are associated with Buddhism. It is only when one gets to the finer points, such as no-soul, rebirth, karma, and so forth, that these dharma principles might be in conflict with what a person's 'religion' teaches them. But Science often conflicts with 'religion' as well. Does this mean that Buddhism should be grouped together with science?
Would one then say, "all science is the same"? Probably not.
Many years ago, a friend of mine, a visitor to the United States from Taiwan, who had been doing some sight-seeing, asked me why, out of all the presidents, Abraham Lincoln was the only one who had a temple devoted to him. At first, I didn't understand, but my friend was referring to the Lincoln Memorial in Washington, D.C, where he saw people coming there (pilgrimage?), talking to the statue, even praying! And if you compare the Lincoln Memorial to some temples in Taiwan, then indeed, Lincoln resembles a large seated Buddha. In fact, the whole structure was designed to resemble an ancient Greek temple.
So, from this person's point of view, this landmark looked like 'religion'.
So, you might ask your friend whether the Lincoln Memorial (or perhaps a similar monument where you live)
is a temple or not, and why or why not.
It is quite likely that, only because of the outward appearance of things,
your friend says 'all religions are the same' (which may be true in some respects)
and from these outward appearances, Buddhism is the same as 'religion'.
But the problem, I think, starts with establishing an abstract category, "religion" and then deciding what constitutes its component features.
Profile Picture: "The Foaming Monk"
The Chinese characters are Fo (buddha) and Ming (bright). The image is of a student of Buddhism, who, imagining himself to be a monk, and not understanding the true meaning of the words takes the sound of the words literally. Likewise, People on web forums sometime seem to be foaming at the mouth. Original painting by P.Volker /used by permission.