If a person tells me they are a 'this' (religion) or a 'that' (religion), I assume very little about them in connection with their self chosen label.
If someone tells me they are a 'Christian', I figure they have some personal connection with SOMETHING typically (or topically) associated with 'Christianity' (though not necessarily in a typical way).
They could have a connection with a church community, the character Jesus, some concept of 'Christhood', the whole (christian) bible, certain parts of 'the bible', standard doctrines and interpretations, their own personal interpretations... etc, and any attitudes ranging from condemnation and judgementalism to acceptance and love/kindness.
When it comes to 'religion' what people say they are doesn't pack a whole lot of information. WHO they are, and what they are actually about (actualizing in their lives) is something I will find out by spending time with and around them. I have no personal need for people's chosen labels to reflect my own ideas. Their labels are their own, to fill and realize as they like.