"So what percentage of Jews actually reject the Talmud?"

That's a good question. An exact percentage can't be taken down or ascertained. This is because of three things:

• Even some Karaites and quite a few Messianic Jews will take parts of the Talmud that are not in contradistinction from Scripture and follow them or implement them--e.g., Hanukkah; the names of the months. By the way, the Pharisee name "Nisan" and Hanukkah both appear in Scripture.
• There are Humanistic and other Jews (e.g., Yaron Yadan) who reject Tanakh altogether because they intertwine it with the Talmud. Yaron Yadan tellingly states, for example, "The prophet Ezekiel contradicts the words of the Torah...Know that this contradiction is found even within the Torah itself, for in Deuteronomy (24:16) it is written, "Parents shall not be put to death for children, nor children be put to death for parents: a person shall be put to death only for his own crime." The Gemara in Sanhedrin 27b reconciles the contradiction: "'visit[s] the guilt of the parents upon the children'! On those who continue their fathers' deeds." That is, the children are punished (for their parents' guilt?) when they continue to sin. See Ibn Ezra on Exodus 20:4, who went on at length about the reconciliation of contradictions." Yaron Yadan himself has the trouble of both separating the Torah from the Talmud, and separating--for instance--individual punishments and curses on the family line as a punishment to the family's partriarch or matriarch--viz. direct and indirect consequences.
• The percentage of Karaite, Messianic, and other--both Patrilineal, Matrilineal, and both-parent--Jews who reject the Talmud entirely can't be ascertained. Om an incidental-but-perhaps-related note, we can't even account for how many Jews were murdered in the Holocaust--usually only Matrilineal Jews who are more than a 1/16th or so Jewish are counted (though Scripture--e.g., Galatians 4:22-24 and 1 Chronicles 7:14--accounts that Isaac was the first Jew, and that Manasseh children were 1/16th Jewish and still Jewish).