(this is gonna come with some tangents and personal experiences represented by footnotes, sorry if that bothers you)
I think it's people trying to separate the extremists from the non-extremists; kinda like how people used to talk about how al-Qaeda or ISIS were "fake Muslims" because they twist the Quran to make it say anything they want. Additionally, I think there's a legitimate argument to be made about whether or not they can truly be considered Christians because of their refusal to accept Jesus' teachings about unconditional love.
I dunno if the situation with Islam/Quran is similar, but the core tentant of Christianity is that you're a follower of Christ and that Christ's teachings are not open to debate and must be followed, regardless of your opinions on what was said before or after him (aka Old Testament or "interpretive" books of the New Testament^1 ). That means if Christ said it, you have to follow it. That means you don't get to be judgemental, you don't get to look down on the homeless or tell people to pull themselves up by their bootstraps, you don't get to be pissy about gay, trans, socialists, communists or any other "-ists" or "-isms" because Jesus taught unconditional love and acceptance.^2
As such, while I understand your stance about fake vs true Christians, I believe that separating people into fake vs true Christians has legitimate value. Again, by definition, Christianity is a religion that revolves around the teachings of Jesus Christ of Nazerath. If you refuse to accept Jesus' teachings then, by definition, you are not a Christian.
(Ironically, you could argue that there are many non-christians who could actually be considered accidental christians if they adhere to the secular parts of Jesus' teachings, though that's a completely different story and mostly based on my personal interpretations of his teachings).
^1 I don't consider myself a Christian anymore, primarily because I think widely-organized religion is cancerous (I think small-scale religious institutes like churches or temples are fine, the problem is when churches, mosques, temples, etc start getting together to dictate belief beyond a church or two). However, there was a brief time during my Christian years where I was taught that the Old and New Testaments were written by humans and were a mix of figurative and literal record. Some stories, like Noah or Job, were almost certainly figurative and meant to be taken as metaphors or moral lessons; while others, like the book of Matthew, were meant to be more literal. Furthermore, because they were written and maintained by humans, they can't be considered 100% accurate simply because humans are imperfect. Even if the original stories were 100% true, they're extremely old and prone to translational mistakes (you can find many disagreements here, a famous one is a disagreement on the anti-homosexuality decree in Leviticus because it could be translated to condemn pederasty instead). You have to piece things together from the variety of sources and contexts presented in the Bible (and if you're a religious scholar, bring in outside sources and historical context too).
As such, I was taught that I needed to apply critical thinking to the Bible and consider what was likely intended by God, and what was human (mis)interpretation; and that the reason why we have so many books of the Bible, sometimes with conflicting statements, is so that we can use them to try and piece together a more accurate picture of what actually happened. If we didn't have multiple perspectives then we'd have to blindly follow a single account and hope it's accurate.
I was taught that I should start with Jesus' teachings and then work outwards in order to properly analyze the Bible, because those are the passages the entire religion is based around. If something conflicted with his teachings, then it was either a flawed interpretation, it was an interpretation that I lacked the historical context for (and is likely irrelevant to me as someone who wasn't a religious scholar, otherwise the context would have probably been included) or it was because his presence was meant to re-write the rules.
Then the church had a conservative "coup" and started teaching brainlessness over thoughtfulness.
Anyway, I'm very aware that my experience was different from the way a lot of churches teach the Bible, but it gave me a radically different perspective on Christianity and it's why I still feel compelled to defend it despite not identifying as one anymore. I saw a side of Christianity that was genuinely interested in teaching love, kindness, acceptance, intelligence and knowledge. I also saw the side of Christianity that got us to where we are today.
^2 I think an argument could be made that the love Christ taught wasn't truly unconditional, but that it was nearly unconditional. The reason for that is, based on my prior stated experience with Christianity, I have a hard time believing that Christ would honestly teach love and tolerance towards practitioners of negative "-isms" like racism or antisemitism.
Christ taught people to turn the other cheek, and (speculatively) I think he'd teach that it's important to be forgiving of those who open their eyes and are repentant of their bigotry. However, I can't see him teaching people to be tolerant of bigotry because that would seem like it'd run counter to the overall theme of his message. If you tolerate bigotry, then wouldn't that make you an accessory to it? After all, your inaction allows bigotry to spread and hold power. Furthermore, if you're an accessory to bigotry, doesn't that make you a bigot yourself? Jesus taught against bigotry, so I think he'd be against tolerating bigotry. I think it's more likely that he'd teach people how to identify, resist, effectively argue with and deprogram people who'd fallen into bigotry.
This was a lot longer than I was expecting, I hope it was an interesting read even if you disagree with it.