As the issue of the rights of transgender people comes more to the foreground, schools across the U.S. have been confronted with a new issue: how to handle gender-specific bathrooms and locker rooms.

A state law passed in California allowing transgender students to use the bathroom of their choice, while some school districts in other parts of the country have been criticized for mandating that students use the facilities of the gender with which they were born.

Most Americans (59 percent) aren't comfortable with the idea of transgender students picking which bathroom or locker room to use, and think they should use the facilities of the gender they were born as, while 26 percent think they should be allowed to use the bathrooms and locker rooms of their preferred gender.

Women (at 29 percent) are slightly more receptive to the idea than men (23 percent).

But there are greater differences by age. Just 23 percent of Americans age 30 and older think transgender students should be able to pick which facilities to use, compared to 35 percent of Americans under 30.

There are political differences as well. Republicans (at 71 percent) are more likely than Democrats (56 percent) and independents (55 percent) to think transgender students should have to use the bathrooms and locker rooms of their birth gender, as are conservatives (69 percent) in comparison to liberals (50 percent) and moderates (55 percent).

This poll was conducted by telephone from March 19-23, 2014 among 1,016adults nationwide. Data collection was conducted on behalf of CBS News by SSRS of Media, Pa. Phone numbers were dialed from samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The error for subgroups may be higher. Interviews were conducted in English and Spanish. This poll release conforms to the Standards of Disclosure of the National Council on Public Polls.