One of the biggest hindrances in apologetics is that we debate things that just don't need to be debated. Take, for example, who/what qualifies as "Christian". This is not something we need to mess around with, it's unbelievably simple. We even see the very origins of the term in Acts 11:26: The disciples were first called Christians in Antioch.
So, this is really very simple. In order to be a Christian, you have to be a disciple. To be a disciple, you need three very important things: The Jesus the Apostles preached, the Spirit Christians receive, and the Gospel the early Church accepted (2 Corinthians 11:4). If you lack any of these, you're not a Christian.
Let's apply this logic to a girl I found on a dating app called Hinge. I've blocked out a lot of details about her location and education, but all the important details are still there. Hinge is somewhat unique in that it actually allows you to select multiple religions, all of which will show up on your profile. Because of this, even though I used to have it set so that only Christians showed up, every now and then, I'd find someone with more than one religion listed. In this case, Christian and atheist. In the past, I have made a similar point about a girl I knew in college who claimed to be a Christian who doesn't believe in God.
Any sensible person can tell you the flaw in this reasoning. It is the very definition of a contradiction! Christianity and atheism are as far apart as the East is from the West. One is about denying God's existence, the other is about worshiping Him. How, then, can one be a Christian and an atheist? This right here is the clearest example of why merely claiming to be a Christian does not make one a Christian, and why pointing out "you're not a Christian because..." is not the No True Scotsman fallacy, as such observations are often claimed to be.
But sometimes it's a lot harder than saying "of course you're not a Christian, you're an atheist". The majority of people who would be classified as non-Christian are not classified as Christians because they believe some fatal heresy, or simply because, regardless of the purity of their doctrine, they don't live as if they believe it.
The most obvious example would be the Mormon Church. This is where the debate is the least heated. Most non-Mormon Theists recognise that Mormonism, though it currently claims to be Christian, is not Christian. But an atheist, an agnostic, and of course a Mormon, might claim that it is. Can we continue to dispute this claim? Yes! Absolutely. Why? Because they have accepted another Jesus, whom the Apostles did not preach. They have a different spirit, whom the Church does not receive. They preach a different gospel, which the Church has never accepted. Mormonism is demonstrably contrary to the Christian scriptures, and therefore cannot be Christian.
From this, we can actually move up the scale to more heated debates. The most obvious example here would be Roman Catholicism. If you say that Catholicism is not Christianity, people will look at you as if you have two heads. But it follows the same logic. Catholicism does affirm the Biblical Jesus, but the spirit of Catholicism is not the Spirit of Christianity, and Paul would say that even if an Apostle, or an angel from Heaven, preached the gospel of Catholicism, they are "anathema", i.e. accursed (Galatians 1:8).
It does get a lot harder when talking about individuals. The thing about religion is only the most devout people know what theirs truly teaches. Sometimes, you can actually cite a person's own religious sources to them, and they'll actually flat out deny these things are a part of their religion. You can have a Christian who claims to be a Mormon, or a Catholic, or any other religion on the planet. As long as all essential elements of Christianity are present, you can still be a Christian. But the logical law of non contradiction necessitates that while you can be a Christian and claim to follow non-Christian religions, you cannot be a Christian and actually follow non-Christian religions. And it is not fallacious to point this out. It is actually fallacious to deny it.
Finally, we need to clarify what is meant by "essential". If perfection was essential for Christianity, no one would be Christian. We all make errors, and thus there must be some margin for error within Christianity. Things like what we have discussed today are essential, because you cannot lack or alter one and still call yourself Christian. But there are other doctrines Christians can disagree on and remain Christian. Things like church governance, order of service, "holy" days, style of worship, various views on Predestination etc. are not essential. You can disagree, and even make blatant errors, yet still remain a Christian, because we are not saved, or condemned, based on these things.
There are many things in our world that need to be debated. What exactly qualifies as Christianity is not one of them. It is nigh impossible to judge a heart, so it is not always easy to tell if a certain individual is a Christian, but when it comes to judging different religions or philosophies, it's rather cut and dry. A religion is either Christian, or it is not, and there is no room for debating that.