NEW YORK (CBSNewYork) — Americans remain divided over the issue of whether transgender people should use the restroom of their birth gender, or of the gender they identify with.

According to a new CBS/New York Times poll, 46 percent of Americans said they believed transgender people should use the bathroom connected to their birth gender, with 41 percent saying they believed transgender people had the right to use the bathroom of the gender they identify as.

However, while the overarching percentages vary by only several points, there are stark differences in beliefs when broken down by demographic, especially within age ranges and political beliefs.

Democrats and liberals are overwhelmingly in support of transgender people using the bathroom they identify with, with 60 percent of Democrats and 71 percent of liberals saying they supported the idea.

On the other side of the aisle, two-thirds of Republicans and 66 percent of conservatives said they believed that transgender people should use the bathroom associated with their birth gender.

Independent voters were split on their view, with 49 percent believing transgender people should use the bathroom associated with their birth gender, and 38 saying they should be able to use the restroom they identify with.

Transgender use of the bathroom based on the gender they identified as was also favored more by younger demographics — those ages 18-29 and 30-44 — as opposed to older demographics — ages 45-64 and those above age 65 — who largely favored transgender use of the bathroom associated with their birth gender.

Men and women were also split on the idea — more women favored transgender use of the bathroom they identify as (46 percent), while more men (51 percent) said they believed that transgender people should use the bathroom associated with their gender.

The issue of transgender bathroom use became a hot-button issue after North Carolina Gov. Pat McCrory signed legislation that invalidated an order in the city of Charlotte allowing transgender people to use restrooms aligned with their gender identity.

The move sparked a flurry of criticism and protests from LGBT advocates as well as from leaders from other states. Musicians like Pearl Jam, Ringo Starr and Bruce Springsteen canceled concerts in North Carolina in protest, while New York Gov. Andrew Cuomo and Connecticut Gov. Dan Malloy issued non-essential travel bans to the state.

Last week, the Obama administration told public schools nationwide Friday that they must allow transgender students to use bathrooms and locker rooms consistent with their gender identity.

In the letter to schools, the Obama administration says “the desire to accommodate others’ discomfort cannot justify a policy that singles out and disadvantages a particular class of students.”

McCrory and fellow Republicans said Obama’s administration went too far by stepping in. The state and the federal government sued each other over the issue earlier this month.

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