As this is the only part of your post that has any relevance to what I said earlier I’ll answer it.
Someone who proclaims a belief in God is not, by definition, an atheist.
So far, so good.
So how could I class him as such? Likewise, someone who says that they don’t believe in God is not, by definition, a Christian.
Here us where you begin to go astray. No, someone who says they “don’t believe in God” may mean by that a number of subtle things.
They may not trust God, which is not necessarily the same as dismissing the existence of God, outright. They may, in fact, be convinced of the existence of God or be agnostic, either of which does not “by definition” make them a Christian, at the same time as they insist they have no “faith” in God – i.e., don’t trust him, whether or not he exists.
It is true that someone who does not believe that God exists cannot be, by definition, a theist, but that doesn’t necessarily mean they are necessarily a Christian if they do believe that God exists. Belief or lack of belief in God’s existence does not mean the person is or is not a Christian, necessarily. It could be true, for example, that even if they don’t believe that God exists they may still be an unintentional “Christian.” What if they are living a life that emulates all the principles that Christ taught and are, whether consciously or not, acting as a follower of Christ? Why would they not be a “Christian,” despite their objections to being called one?
So I certainly wouldn’t include him or her in the set of Catholics I use to determine the beliefs of Catholicism.
I would object to your negative characterization with regard to what makes someone a Christian or Catholic. AND I would still object that it isn’t simply a matter of self-identification because anyone could claim to being either Christian or Catholic for a number of illicit reasons, which renders the reality of what it means to actually be one, null.
I mean if you want to make self-identification the standard for actually being something, then I self-identify as a genius. Does that alone make me one? If it does, then it would, at the same time, render meaningless the actual meaning of what it means to be that thing.
Furthermore, you are attempting to make a negative case by claiming someone who doesn’t “believe” in God CANNOT, by definition, be a Christian, but that avoids completely the issue of what it actually means to be one. Again, a problem for your negative characterization.
As for the rest of Christian, and specifically Catholic beliefs, I leave it to the individual to decide how they class themselves. It’s not a decision I am in a position to determine. Maybe you are.
If neither you nor I are in the position to determine whether someone is a Christian or Catholic, I would suppose that would mean, that neither is the one claiming to be Christian or Catholic “in a position to determine” whether they themselves actually are. I mean what makes them any more competent than either you or I if the task is so completely beyond either of us – in particular, beyond the capacity of rational rats to make the relevant determinations?
At the very least, we ought to be asking why these self-ascribed individuals think they are Christian or Catholic and if they show sufficiently good cause to be considered either, then we can use their justification to then make a proper assessment with regard to everyone else. Shouldn’t the claimant need to demonstrate their competency, beyond yours or mine, to make the determination before we agree to put them in the “position to determine” without possible embarrassment whether they are or are not?
Which is my position, essentially. I wouldn’t suppose any of us can make such a claim about anyone else, or about ourselves, which is why I suggest the best judge of whether someone is or is not a Christian or Catholic is God alone.
I would also suggest that it is possible to lay down clear Christian or Catholic principles for what it would take to be one or the other. Otherwise, both terms are essentially meaningless. Now whether or not anyone happens to fit perfectly all of those principles I would willingly leave to God and insist is beyond my paygrade, even with regard to self-identification.
Ergo, we can be competent to compile a set of principles for what it means to “be” Christian or Catholic (the CCC, for example,) all the while expressing complete reticence regarding determining who specifically meets those principles to a degree sufficient to be called or call oneself, for that matter, one or the other.
In short, if you or I are not competent to use the labels Christian or Catholic with regard to any specific individuals, then neither are self-described “Christians” or “Catholics” necessarily any more competent to apply either label to themselves.
Personally, I would be far more comfortable with the majority or people actually being Christian or Catholic, even while renouncing claims to being either, than having a bunch of pretenders walking around calling themselves either while flaccidly or “loosely” following what it actually means to be either.