What 'counts' (and what doesn't)?
On what basis can someone else say that someone is not an adherent of said religion?
This could be about any religion, or indeed the question of adherence/belonging/identification with any other group.
Roughly speaking, there seem to be two conflicting (opposed even) main takes on the matter.
The first view is that religion is supposed to be an unifying tradition and a main trait of families and wider communities. By this take, it is inherited and adherence is assumed unless specifically rebelled against, be it by neglect, heresy/splitting out, open abandonment or conversion to some other Faith. While popular, it has the serious drawback of demanding people to accept labels until and unless they object to them. It sacrifices meaningfulness to benefit demographic spread and, granted, social bonding.
The second view is that adherence to a religion is supposed to be conscious, voluntary and personally meaningful.
While the first is far more widespread, I think it melds cultural and religious matters far too much to be meaningful. So does the second, to a degree.
My personal criterium is that while people can and should learn about various religions, meaningful adherence can only be attained by, for practical purposes, becoming one's own priest and religious authority and deciding matters of doctrine on a personal level. It is for the practicioner to give credence to the religion, not the other way around.
My view runs against the grain of the traditional role of religion as a core element of social identity, but all the same I find it overall more meaningful and more productive than the alternatives.