Word PSA

right, n. That to which one has a just claim. (1913 Webster)

rite, n. The act of performing divine or solemn service, as established by law, precept, or custom; a formal act of religion or other solemn duty; a solemn observance; a ceremony; as, the rites of freemasonry. (Op. cit.)

There can certainly be such a thing as a "right of passage" (for example, if I contracted with you to build and use a road across your property, I would have a just claim to build and use that road).

But usually when I come across the phrase "right of passage," what's actually being referred to is a "rite of passage" -- some act or event seen as ceremonially/ritually marking a change point in a person's status from childhood to adulthood, amateur to professional, etc.