The Makriv is Part of the Korban.

Both Jews and Gentiles can bring sacrifices to the Beis Hamikdash.  But there is an important difference between them.
A Jew who is an idolater is not allowed to bring any  Korban to the Beis Hamikdash.  (Chulin 5a, and Eiruvin perek Hadar)  On the other hand, a Gentile that is an idolater is allowed to bring a Korban.  מכם ולא כולכם להוציא את המומר מכם בכם חלקתי ולא באומות.  When I said this Gemara, my shiur expressed their surprise.  How can it be that we are more machmir by the Korban of a Jew than that of a non-Jew?  What is the logic of the distinction?  If a requirement for accepting a person's Korban is that he has at least a fundamental faith in God, why doesn't that matter when a Gentile brings a Korban?  If a corrupted owner corrupts the animal, what difference does it make who the owner is?  Gentiles are just as tainted by Idolatry as Jews are.  

(The members of the shiur offered two answers.
1.  We only accept the Korban of a Gentile mipnei darkei shalom, to show respect and to avoid antagonizing them, but it's not really a Korban.  That is false, period.  It's a korban and it has halachos of korban.
2.  It's not such a sin for a Gentile to be an idolater.  False again.  It's a capital offense, and that's pretty serious.  Also, it's illogical. Why would it be less of a sin for a Gentile to be an idolater?  They have just as much of a duty to recognize the Ribono shel Olam as we do.  They are not just the extras in our movie.)

The Oneg Yomtov's Answer

See Oneg Yomtov in middle of note on the bottom in #45, who asks this question.  

His first answer is that if the Kohanim doing the avoda in the Mikdash are acting as our agents  (שלוחי דידן, Nedarim 35b,) then this halacha makes sense, because according to our halacha, there is no law of agency by Gentiles, and if the Torah said you take korbanos from Gentiles despite the the general rule that the is no din of shlichus by Gentiles, then apparently a Gentile's Korban does not need the Agency that is required by a Jew's Korban.  If the Kohanim are not bringing his korban as his agents, then we don't care if he's an idolater.  On the other hand, by a Jew, for whom the Kohanim are acting as Shlichim, as his  agents, it is he who is bringing the Korban, and therefore his status matters.

But he says that this answer won't work according to the Rambam that paskens that even in a Yisrael's Korban, Kohanim never are acting as the principal's agent (שלוחי דשמיא).  He reiterates the question: how can it be that we accept from Akum mumar but not Yisrael mumar.  It's illogical; the Gemara itself had rejected this idea in a different context (regarding regular shechita of Chulin animals-השתא שחיטת מין דישראל אסורה דעובדי כוכבים מיבעיא), and if it's such an apparently illogical svara, and there is an alternative ways to darshen the passuk by Kodshim, how can the Gemara let such a drasha stand?

He answers that even if the Kohen is not the person's agent, there is still a difference between Korban Yisrael and Korban Akum.  By a Yisrael's Korban, there is Semicha, leaning on the animal before Shechita, and there is no such act by a Korban Akum.  Perhaps it is because of the din of Semicha by a Jew's Korban that we don't allow a Mumar to bring a Korban.  But he finds fault with this answer as well.  He that if the basis of not allowing a idolatrous Jew to bring a Korban is that we can't allow him to do Semicha, then a mumar should be able to be makriv bechor and maaser (and ofos), korbanos that have no Semicha.

I don't know why he didn't mention a bigger hole in his pshat- that according to him, a woman who is a mumeres should be able to bring a korban!  And if you're going to answer that he means that since men do semicha, you see that the nature of the korban is such that it is in the parsha of semicha, then what's bothering him about Bechor and Maaser?  And what about Korban Ofos, bird korbanos?  There's no smicha there.

Another little question on his teretz is from the Gemara in Temura 2a.  Machlokes RM and RY; RM- does do semicha.  RY- No he does not.  According to RM, also a group korban has semicha from every participant.  RY- three times it says Korbano.  One to exclude non-Jew ( to tell you that not even the Kohen should do Semicha on a goy's korban,) one to exclude someone else's korban, and one to exclude Yoreish.  Alternatively, he uses on drasha to exclude someone else's and a goy's, because the idea is that there is no shlichus for semicha (because we know from elsewhere that the goy himself doesn't do it.)

So according to his teretz, you could say a chiddush that a yoreish who is a mumar should be able to bring his father's korban according to Rav Yehuda.  


The Brisker Rov's Distinction

The Gemara in Zevachim 45b says that the tzitz is not meratzeh by the korban of a goy because by korbanos it says it says Leratzon lahem, and not for akum; since Ritzui Tzitz has to do with Ritzui, and there's no Ritzui by akum, so there's no din of tzitz by their korbanos.
The Brisker Rov there in Zevachim 45 says that you shouldn't make the mistake of thinking that the reason there's no din tzitz by korban akum is because ritzui tzitz is a din hartza'a which doesn't exist by akum.  That's not the pshat.  The pshat is that the whole korban akum is not coming for hartza'a, so ritzui tzitz is irrelevant and cannot be mattir the Korban.  With this, too, we understand why Korban Akum is not a problem.  The exclusion of a mumar only applies to a korban of ritzui.

The Brisker Rov's opinion can be viewed in a sefer of Reb Dovid's shiurim.  Also, from another sefer, quoting the Rav,

 דר״ש ס״ל דקדשי עכו״ם חלוקים בעצם החפצא מקדשי ישראל, דיש קדושה של קרבן ישראל ויש קדושה של קרבן עכו״ם, וילפינן לה מדכתיב בקרבנות דבר אל בני ישראל, וכמש״כ הרמב״ם בהל׳ מעילה (פ״ה הל׳ טו), אבל רבי יוסי ס״ל דאין חילוק בעצם החפצא ביניהם, משום דכתיב בהו לה׳, וקדושה אחת להם, ומשו״ה א״א לחלק ביניהם לגבי הדינים שחילק ר״ש. וזהו מה שמקשה הגמי, דהברייתא דאין ציץ מרצה על קרבנות עכו״ם היא דלא כר׳ יוסי, דקס״ד דדין זה הוא ג״כ משום שלקרבן עכו״ם ישנה קדושה אחרת, ומשני דבזה גם ר״י מודה, דהא דאין ציץ מרצה על קרבנותיהם אינו מחמת דין הקדשם, אלא הוא מיעוט בבעלים של הקרבנות, דבריצוי ציץ כתיב לרצון להם, ועכו״ם לאו בני ריצוי נינהו.

(ועיי״ש שהוכיח מפירוש הר״ש משנ״ץ על התו״כ ( בפרש ת אחרי פרשתא ז הלכה ה דבקרבנות עכו״ם ליכא הרצאת קרבן, דאינם לרצון ל פ נ , ה' , ונתרבו רק לענין שיכולים להביא קרבן. אבל הקרבן אינו מרצה כלל על הבעלים, ולפיכך גם הציץ אינו מרצה על הדם שנטמא, דריצוי ציץ לא נאמר אלא בקרבנות שיש בהם הרצאת בעלים עכ״ד

My Proposed Answer

So, let's get back to our question. 
You have the Oneg Yomtov that says that even if you hold shluchi derachmana, that's only by korban yisrael, not by korban akum.  Also, you have the Gemara in Zevachim says that there's no ritzui by korban akum.  And we have the general dinim that there is no semicha or vidui by the Korban of a Gentile.

I want to explain, in baalebatishe words, what the yesod of the difference is, and, like in Reb Moshe's approach, it explains many of the differences in halacha between Korban Yisrael and Korban Akum.

The difference is that when a Yisrael brings a korban, he is part of the korban.  The makriv is part of the yesod of the korban, just as kehuna, and kli shareis, and me'kom hamizbei'ach are parts of the dinim of the korban.  When a yisrael does smicha it is because he is the korban too, except we don't shecht him.  He is the part that we don't shecht or burn on the mizbei'ach.  He has ritzui because the Zerikas Hadam created a din of ritzui on the Korban, and he is a part of the Korban.  By akum, the makriv is not part of the korban.  He is the person who donated the korban.  Therefore, while he is doing a good thing, there is no din ritzui, a din which is exclusively related to a Korban.  (There's no need to extend this, and it causes more problems than it's worth, but one might relate this to the din that the special Din Shlichus the Torah creates by a Yisrael does not exist by Akum.)

This concept appears in the Gemara in, for example, Taanis 26a, where the Gemara says

אלו הן מעמדות לפי שנאמר (במדבר כח) צו את בני ישראל את קרבני לחמי וכי היאך קרבנו של אדם קרב והוא אינו עומד על גביו התקינו נביאים הראשונים עשרים וארבעה משמרות על כל משמר ומשמר היה מעמד בירושלים של כהנים של לוים ושל ישראלים 

The Netziv finds a source for this halacha in the passuk in Balak, where Bilaam told Balak to stand at the altars while his Korbanos were being brought.

With this, I just want to suggest that unlike other korbanos, where if a mumar brings it, it is just passul, it could be that if a mumar brings Ketores, there's a bigger problem.  I think that if a mumar brings ketores, it has a din of חיסר אחת מכל סממניה חייב מיתה (Kerisus 6a), if one leaves out one ingredient of the ketores, he is subject to the death penalty.  The makriv is one of the ingredients of the ketores, too, and if he's a mumar, he's chayav missa.  I've found this svara to be quite useful, and have used it in many places in Kodshim.

I don't know if you need more reasons why the 250 people of Korach died after bringing the Ketores, but if you do, now you have one.

With this in mind, please see the post in Pekudei that explains the lomdus of the Korban of a Yisrael, and the tremendous chiddush of the Akeida.
Turns Out To Be a Machlokes Between the Chazon Yechezkel and the Brisker Rov.

After writing this, I spoke to my son Shlomo, a Brisker.  He told me that this is a machlokes between the Chazon Yechezkel and the Brisker Rov.  The Chazon Yechezkel, in the beginning of Zevachim, says that the pshat in Shelo Lishma is that it becomes a korban without a Baalim.  The Brisker Rov said that is impossible.  It is impossible to have a korban without a Baalim.  Rev Michel Feinstein (the Rov's son in law) tries to make a lomdishe yes and no hybrid of yes and no baalim.  But the point is that in Brisk, the Rov's svara is talked about as being that the Baalim is a cheilek of the Korban.  So I didn't discover America.

The Chazon Yechezkel is here, at the end of the page, DH אלא שלא עלו לבעלים, and the following pages, where he brings the Brisker Rov's questions and deals with them.  The Brisker Rov's opinion is not printed anywhere in the official Brisker Sefarim, but it is in the shiurim they say in the Brisker Yeshivos.


Reb Moshe's Answer

And here is how Reb Moshe answers the question, in his Dibros on Chulin.  The derech we're discussing is on the next page, except that he doesn't go as far as I do regarding the lomdus of the difference.  He goes on to use this approach to explain many of the differences in halacha between Korban Yisrael and Korban Akum.  This is not the first time I found a whole sugya encapsulated in one paragraph in the Dibros.   אפילו ספר תורה שבהיכל צריך מזל.