Well, there is Hindu, the tag placed upon people that come from
a particular set of cultures that says "this is your religious
affiliation" because many of the practices appear to fit a
certain mold of "This is Hindu" by those who are doing the
tagging...
...and then there is Hinduism which is a family of belief
systems and logic systems that historically came from a family
of cultures but is ALSO Universal in scope. Sometimes they
coincide, sometimes they don't.
Growing up in a one square mile town in NJ where you were either
went to the Protestant Church (which was Methodist) or went to
the Roman Catholic Church... [as a kid, we knew of no other
possibilities, at least with the kids and families I knew] - I
went to the Methodist church because to my mom it was "close
enough". I enjoyed it and helped form a lot of my assumptions
about things.
Among my Catholic (both Italian Catholic *and* Irish Catholic -
NJ isn't "mostly Italian" by the way - silly stereotype, nor do
they talk like you hear on TV) friends, some didn't know they
were Catholic. They just went to church and did their thing.
Some families didn't to church and when pressed by someone,
they'd say, "Oh well, my grandparents go to that church over
there, so I guess I'm Catholic, I dunno".
So, I think there's room for both a cultural religious tag and
also a deeply held belief system that can be abstracted somewhat
from its culture of origin and universalized, making it
accessible to a larger population than just people who happened
to be born in a particular family with particular traditions.