Please don't take anything I say here as intended to be insulting. I am only anzswering your questions.
I would not presume to judge the eternal destiny of anyone at all. That's God's job alone. However, it seems there are some objective norms that should be followed, even if those norms can admit to "exceptions."
If Jesus established auricular confession as the ordinary means of seculring God's forgiveness of sin, then it is to be followed, certainly as a norm. As it is, the Church has taught that "perfect contrition" for sin, even outside of confession, can suffice, particularly when the circumstances allow for no alternative at the present time for the person (e.g.: imminent chance of death, no priest available). In other words, there is an "exception" to the standard. But the standard remains, nevertheless, and, should one find himself out of danger, he should avail himself of recourse to that standard means. Issues regarding other Catholic practices and Sacraments, such as the Eucharist, have similar considerations regarding objective "norms" and the subjective "good intentions" of non-Catholic/Orthodox Christians.
This sort of approach applies in full vigor to Catholics (and Orthodox, of cousre), since these things are available to them. Objectively, it applies to every Christian, but there is a subjective component of complete lack of availability - through invincible ignorance, sheer denial of the requirement based on insufficient understanding, etc. - that we believe God takes into account.
But, at this point the question becomes: "well, if there's this subjective component involved, I don't really need these Catholic trappings, right?" I would say that is an entirely incorrect stance to take, from a Catholic POV.
First of all, we Catholics believe that Sacraments are vehicles for God's grace. In fact, they are the primary means through which He dispenses His sanctifying grace, without which no one can be saved. If He dispenses sanctifying grace through other means, He is certainly free to do so. He is God, and, as the old saying goes, "God is the Author of the Sacraments, but He is not bound by them." Fair enough. But He has not been all that explicit about how He does this outside of the Sacraments, too. It is therefore a much more vague and tentative proposition for a Christian to be in receipt of snctifying grace outside of the Sacraments, even while the possibility is acknowledged.
Second, without the "assurance" of forgiveness of sin through sacramental confession of sins, or the relative assurance that, in the present here-and-now one is objectively in a state of sanctifying grace, and that one is capable of receiving further grace through the worthy reception of the Eucharist, or, as circumstances allow, another Sacrament, one can presume very much regarding how his soul stacks up from God's POV. We reject the notion that one attains salvation in some discrete moment and cannot possibly lose it afterward. This applies to every Christian, not just Catholics, from our POV. So, it is something of a dangerous proposition to go through life - especially in these times fraught with unprecedented temptations to sin - without the assurances of grace through the vehicles that God has appointed for dispensing that grace. It would be very difficult indeed for a Christian to pull himself all the way through a lifetime in any part of the Christian Era without the assured dispensing of His sanctifying grace; it is doubly hard today, no doubt. Therefore, while we don't deny that God "can find a way" to save non-Catholics who do not and cannot receive sacramental grace, we clearly believe is it far more advantageous, and far less speculative, if one can go through life with the "ordinary means" at his disposal.
Which brings me to a third point. As I said earlier, everyone must die in a state of grace (put simply, without mortal sin - or "deadly" sin, as described in 1John 5:16-17 - in order to enter Heaven. The "mortal" designation refers to the "spiritual death" of damnation for those who die their physical death while in that state of sin. None of us who has lived past the age of reason (generally understood to be around 7 years of age) goes through life free of sin. All of us need forgiveness. If we don't secure it by the normative means that Christ established in confession and/or the anointing James speaks of in James 5:14-15 (or even baptism itself, should we subsequently not sin again, and die in its grace, though this would be a rare occurence unless one old enough to be responsible for his actions is baptized immediately before death), then there is nothing left except to try to make what we Catholics call a "perfect act of contrition." But, that is a very hard thing to do. The contrition is based entirely on sorrow for offending God because of Who He is, and not in any part out of fear of Hell and punishment. Most people approach confession with "imperfect contrition," with perhaps an admixture of sorrow based on repentance for offending God per se, and also fear of punishment. The normative nature of the Sacrament obtains forgiveness anyway. But, in its absence, one must meet a stricter standard, if you will. It is not God's fault that one finds himself at death's door and has not availed himself of the means that God Himself has established.
As I said, this type of contrition is very difficult. It must be based on sorrow for offending God alone, and even all attachment to sin must be abandoned. That, too, is very hard. So, from a Catholic POV, it is a far riskier and more speculative proposition to suppose that non-Catholics, who have never received the normative means of sanctifying grace outside of baptism, should presume to be in a state of grace at death. If they are not, they cannot be saved by definition, per 1 John 5, as above.
So, to summarize an answer to your question, based on considerations I've just stated, I would say that, while it is possible for non-Catholic Christians to be saved - because nothing is impossible with God - the normative means of forgiveness and grace He established are still vitally important, for they provide a moral assurance that we have been forgiven, are receiving His grace through worthy reception of His Sacraments, and have a much better "shot" at a favorable judgment if we die availing ourselves of those means, or recently availing ourselves of them and committing no subsequent, serious sin.
Our bottom-line is: yes, maybe you will die in a state of grace, but, unless God delivers sanctifying grace to your soul and you die truly and perfectly contrite, you will not. And, outside His own established "norms," how will you know?
Finally, I would just say that your question: "Is there anything we lose in eternity because of our choice of denomination, from a Catholic perspective" is simply too speculative. If anyone gets to Heaven at all, it is because of the mercy and grace of God. Their reward will be based on their relative love of God in this life, and how that motivated them, through His grace, to serve Him faithfully. I don't doubt for a second that some non-Catholic Christians are in Heaven, and that some of them are in a higher state of blessedness and happiness than some Catholics. But, again, it's so much harder to get there in the first place for non-Catholics deprived of the Sacraments, from a Catholic POV. Therefore, to answer what you ask next: "Does the choice matter," I would say: yes, it certainly does.
Again, I apologize if this seems offensive somehow. I suppose that it could easily be misconstrued that way, but that is sincerely not my intention. I am only answering your question regarding how we Catholics still allow for the possibility of salvation for non-Catholics, in spite of what we say regarding the Sacraments and their necessity.
I found nothing offensive in what you wrote. Of course, I asked the question.
In general, I expect people to defend their own faith. And I would think that people believe that their faith is correct.
In fact, in this discussion, I felt like people were too quick to be disturbed, although I understood it. But if I read a title “Can Presbyterians be Christians”, I wouldn’t think “Oh no, someone thinks I’m not a Christian”, I would say “Oh, I can see how someone of another belief system feels about my belief system”.
So instead of being upset, I would welcome the opportunity to see how other denominations think about my faith, rather than get upset about what they believe. After all, I don’t believe that other denomination has their beliefs correct, so why would I think their beliefs about my denomination would be correct?
So I asked my questions, because I wanted to see how some of those participating in this discussion would address a different faith from their faith’s perspective. You did a wonderful job. As did others who responded to me, I read them all even though I didn’t answer them.
I hope those who participated will have read these responses, and realised that talking about other faiths from your perspective will of necessity sound somewhat judgmental, or something like that, and try to take it in the spirit of ecumenicalism, rather than as an attack on their faith.