WASHINGTON — The two most influential social liberals in President Trump’s inner circle — daughter Ivanka and son-in-law Jared Kushner — helped kill a proposed executive order that would have scrapped Obama-era L.G.B.T. protections, according to people familiar with the issue.

A third, Gary D. Cohn, the chairman of the president’s National Economic Council, a Democrat who was brought to the West Wing by Mr. Kushner and reflects the socially liberal and economically conservative views of many Wall Street power brokers, privately told aides to the president that he was disturbed it was even being considered.

The executive order has exposed what is likely to be a persistent schism in Mr. Trump’s paradoxical presidency: He is a cosmopolitan New Yorker who has long operated in an environment where sexual orientation is often an afterthought, but is nonetheless beholden to the social conservatives who backed him overwhelmingly in 2016, despite reports of his crudeness and sexual misdeeds.

Mr. Kushner, a lifelong Democrat, and Ms. Trump, an independent, travel in liberal social circles and have long supported L.G.B.T. rights. Neither had seen the order before details were leaked. They expressed their dissatisfaction to Mr. Trump’s other advisers, and then weighed in directly with the president, who opposes same-sex marriage but has spoken out against discrimination.