the status of a baby born of a sperm donation from a Jewish donor to a non-Jewish mother

A person who's mother was a gentile, and did not undergo Giur (Jewish conversion procedure), is defined Halachically as a gentile for all (halachic-medical) intents and purposes

Nevertheless, Jewish law recognizes the fact that the biological father  is Jewish, so many Poskim encouraged the Giur of such children that are biologically descendant from a Jewish father.
Sources:

1. Responsa of Rabbi Azriel Hildesheimer, Vol. I, Yoreh De'ah, sections 229-230.
2. Mishpetei Uziel –  Responsa of Chief Rabbi (Rishon le'Zion) Ben-Zion Meir Hai Uziel – Vol. I, Yoreh De'ah, section 58.
3. Rabbi Moshe Shmuel Glasner – chief rabbi of Klausenburg (Cluj) – quoted in Responsa Yad Rama (Rabbi Moses Hirsch Fuchs), Even HaEzer, section 11.

 In summary, if you wholeheartedly wish to undergo Giur, it is our estimation that the orthodox Batei Din will not prevent you from accomplishing this.