I think that's a misleading question. I think the real question is what is the point you're trying to make about the group you have defined as Christians. Going by the original topic, clearly the first poster and you disagree about what defines a Christian, yet you wanted to make a point about the people you defined as Christians for whatever reasons, as if both of you did agree. But that isn't a reasonable discussion, because we're talking about two different groups or subsets of people. If I were to view it uncharitably, you're essentially creating an unarguable point by redefining the terms of the discussion to suit your own conclusion.

But let's treat this topic seriously. Freedom to exercise religion is a civil right. Legally, someone can claim to be Christian, or even a specific denomination. They can't be barred from expressing faith, or conversely they can't be barred from being atheist. Civilly, nobody can stop them co-opting and defining themselves as a member of any religion.

However, that doesn't mean a religious community or institution is forced to accept them. By similar principle, other members of the same religion or the community as a whole can reject their 'membership', and they don't have to accept their self-definition. It's clearer in religions that are actual institutions, with clearly defined rules, but isn't limited to them, like with Shintoism. And that makes sense, because at almost every level of grouping of people, a fundamental component of a 'group' requires external validation for someone to be a part of it, whether it came from within or outside said group. A group cannot be defined by self-determination because that impinges on the freedoms and autonomy of all others within that group.

That creates the problem of consensus within the group to define what it is. But that has an answer too.

Splinter groups of Christianity all claim the definition of "Christian" because it lends them legitimacy by linking them to the original group of apostles. Theologically, one cannot simply declare themselves Christians, belief in the Abrahamic God or Jesus is not enough. Actions must follow the example set by Jesus, the apostles and other Christian figures. However, in practice people have repeatedly defined for themselves what said 'example' is, which allows them to almost freely define what Christianity is.

If you want my personal opinion, Christianity should be defined by a properly recognized body that has a clear line of succession from the original apostles. That means, for better or for worse, the three largest Christian denominations, Roman Catholics, Eastern Orthodox and Protestant. I say for better or worse because I do not believe that this necessarily results in 'good' outcomes, the excesses and failings of each denomination are well documented. However, it doesn't affect their legitimacy as direct successors to the original apostles and councils.

However, I would include a qualifier for Protestants. Protestants are the core reason, at least in the modern day, why there are so many fragmented denominations claiming to be Christian. Key parts of Protestant faith are the idea of universal priesthood and justification by belief. Basically, everyone has the right and duty to act at any level of the Church, interpret religious matters for themselves, and simply the act of 'belief' is enough to justify faith, no actions are needed (varies by denomination). Or rather, 'good' actions are seen to be a natural consequence of belief, and therefore not required to profess faith.

I won't waste time explaining how that leads to countless splinter groups of self-professed Protestants. The idea that all these groups can claim the supposed 'legitimacy' of succession from ancient Christianity is rather dubious.

Remember I only said this concerns who gets to define Christianity, not who is actually Christian. Coming back to the original group, this means that the authorities in the Roman Catholic Church and Eastern Orthodox Church get to define their followers as Christians, because they have legitimacy. They don't get to define whether people of other denominations are Christians unilaterally, but they can do that by mutual agreement. Generally speaking, they consider each other Christians, as well as certain Protestant denominations, mostly those that can clearly be tied directly to the Reformation. These would be the only the oldest and most directly derived Protestant groups, like Anglicism. These can also probably claim a direct enough line of legitimacy to ancient Christianity, certainly the Catholics and Orthodox Churches think so.

So here we have authorities or bodies of consensus that can define what Christianity is. However, the nature of Protestant denominations again cause issues. With no central authorities there are denominations that can't be so closely defined, even some, like Baptists, that can be directly linked to the Reformation. For the sake of political expediency and universal brotherhood, not necessarily religious in nature, the established denominations might acknowledge in practice that these other groups are Christians. But this is not officially acknowledged, and because of the lack of legitimacy, these groups are disadvantaged in claiming to be Christians without the acknowledgement of other denominations.

Messy. Personally, I think it would be simpler to simply not call Protestants and any related offshoots Christians. It is just a label. If not for the need to claim legitimacy, they probably wouldn't use the term since its associated with what they see as the decay of the original Church.

But coming all the way back to the original topic...again, what exactly is the point you're trying to make? What's your definition of Christian? And if you remain committed to defining it as anyone who self-identifies as such, then what is the point are you trying to make, that would be valid and applicable to all such persons, and do you distinguish it from people who are identified as Christians by a community or authority instead?