According to the Wiki...
Paltrow was born in Los Angeles, California, the daughter of Blythe Danner, an actress, and Bruce Paltrow, a film and television director and producer. Paltrow’s father was of Ashkenazi Russian Jewish descent; her mother is a Quaker of Pennsylvania Dutch and more distant white Barbadian ancestry. Paltrow’s paternal great-great-grandfather, whose surname was “Paltrowicz”, was a rabbi in Nowogród, Poland. Paltrow has a younger brother, Jake Paltrow, and is a half-cousin of actress Katherine Moennig, and a second cousin of Congresswoman Gabrielle Giffords (AZ-08).
Even thought her Jewishness comes from her father’s side, technically making her not Jewish, she still feels the pull to teach her the ways of Torah.
fine and dandy , but she’ll need a halachic conversion
Paltrow Gets Serious about Jewish Roots
http://www.sfgate.com/cgi-bin/blogs/dailydish/detail?entry_id=2398
Gwyneth Paltrow has started taking her Jewish roots seriously after missing out on two years of fasting during the religion’s high holy days.
The actress was pregnant with baby Apple in 2003 and breastfeeding her daughter in 2004, so she made sure she honored Rosh Hashanah and Yom Kippur in style in 2005.
And Paltrow plans to pay tribute to her ancestors every year from now on.
She says, “I am the result of generations and generations of rabbis back in Minsk. They call it a rabbinical dynasty.”
Pennsylvania Dutch are German-Swiss Mennonites and Amish. They have little overlap with Quakers.
White Barbados ancestry almost surely means Jewish, via Holland and Portugal.
Only according to the Rabbis;
shalom b'SHEM Yah'shua HaMashiach
YHvH in His WORD counts lineage
only through the Fathers.