Beginning next year, transgender students in California schools will be able to compete on sports teams and use facilities, including restrooms, based on their gender identity rather than their sex.

  Schools will have to open up their programs and facilities so that girls who identify themselves as boys are allowed to join boys' teams and programs, and vice versa.   "All students should have the opportunity to fully participate and succeed in school," said Evan Westrup, a spokesman for Gov. Jerry Brown, who signed the new policy into law Monday.   The measure, which takes effect Jan. 1, is intended to reduce bullying in schools and help transgender students feel more comfortable on campuses, said its author, Assemblyman Tom Ammiano (D-San Francisco).   "While many California schoolchildren are already protected by policies in some of our biggest school districts," Ammiano said, "other districts don't seem to understand that transgender students should have equal access to all programs and facilities."   Republican lawmakers and conservative groups had opposed the bill, saying it infringed on students' privacy rights because girls might not want biological males sharing their shower rooms and changing areas.