And he took curd, and milk, and the calf which he had dressed, and set it before them; and he stood by them under the tree, and they did eat.
Looks like Abraham and 3 mysterious visitors don't mind eating mixed milk and calf. If Jews don't eat cheeseburgers, why did Abraham serve a calf with milk?
I do not have the precise location but I was taught that the Yalkut Yoseph brings down eight answers/considerations to this question. Here are some highlights:
According to Rashi the milk was served first which is entirely permissable. According to the Maharal, Avraham only fulfilled the positive commandments while the Gra brings opinions that he wasn't particular regarding Rabbinic commandments (there is no indication the meat and dairy where cooked together which would constitute a Torah prohibition). And regardless of his own observance, the Shita Mekubetzus points out he thought they were b'nei Noach [non-Jews who are not obligated to separate meat and dairy].
Of course this was before the Torah was given so the question doesn't really begin if one takes a minimalist approach to the question of whether the Avos kept the mitzvos.
The Malbim explains that he created a calf using Sefer Yetzirah which can be eaten with milk.
http://hebrewbooks.org/pdfpager.aspx?req=40102&st=&pgnum=168
The Ramban understands that Avraham knew they were angels (Ramban 18:3 s.v. אד-ני אם). If so, this would make it OK to serve them milk and meat. This would also explain why he was OK serving milk and meat but not serving something impure (see Rashi about not serving the dough) because angels are holy (refered to as kedoshim) and holiness is incompatible with impurity (impurity cannot be brought into holy places).
Look at the order -- first milk, then meat. One can have milk, wash out his mouth, wait a period of time (discussed in poskim) and have meat. Which is what some are noheg for Shavuot when dairy is served and then meat.
The following is not profound but it is the simplest answer to a simple question, that does not seem to have been clearly explicated:
Abraham could serve them whatever he wanted (except for a limb torn off of a live animal) since the Torah which is interpreted as prohibiting meat cooked in milk had not yet been given.
Although one will find stray comments attributing observance of post-Sinaic laws to various pre-Sinaic characters, these do not seem to have been the intent of the OP, so addressing them is really irrelevant.
That being said, essentially all post-Talmudic commentators who focus on the simple textually supportable understanding of Scripture, emphasize that these aforementioned statements about pre-Sinaic behavior are homiletic in nature. Some clarify that the intent is to their general upstanding ethical status.
L'insegnamento è che Avrahàm conosceva la Torah, e sapeva che i visitatori avrebbero assunto latte e carne nelle giuste distanze, questo sottolinea che essi si tratte nettero molto a lungo. Il passo è un tamrur azor che ci obbliga a riflettere sulla temporalità del racconto.
Translation from Google (I hope this can be improved upon):
The teaching is that Avraham knew the Torah, and knew that visitors would take milk and meat in the right distances, this underlines that they are learned cleanse very long. The step is a stop sign that forces us to reflect on the temporality of the story.
Shalom
