Why are atheists so willing to believe that anyone who claims to be religious also is religious?
You're apparently suggesting that there's some significance to the phrase "is religious" that eludes many/all atheists. Something that goes beyond mere assertions of one's own religiosity.
Maybe some atheists don't acknowledge this thing because they don't share the idea that religion
should be something more. (Whatever that something is.)
I guess that I'd say that religion is kind of like a rope, composed of numerous semi-distinct strands --
There's belief in propositional doctrines of a world-viewish sort and often about super-mundane realities. There's personal practice, both inward and outward. There's often some ideal of personal transformation. There may be ideas of salvation, of transcendental escapes from life's suffering and from the certainty of ultimate death. There will probably be a social practice dimension, probably including groups performing ritual actions. There may be an assumption that religious practice influences individual and community flourishing here in this life. There's likely an aesthetic dimension. There's almost certainly going to be a difficult-to-describe emotional aspect, all the sometimes overwhelming feelings that accompany religiosity. And obviously there's a critically important ethical dimension in most cases.
Religion probably isn't so much an essence as it's a family-resemblance deal. Perhaps few individual instances of religiosity display all of these aspects, certainly not equally. But individual examples display enough of them that they resemble religion and are identified as such.
So, who is really religious and who isn't? It's a question that atheists should probably take some interest in, for sociological reasons at least.
Maybe I'd say that a person becomes more religious the more of these aspects that they display. (Adjusted for their particular tradition, which may emphasize some and deemphasize others.) And maybe more important, a person becomes more religious as these aspects become more central in their lives and the focus of their daily activities.