Updated: 5:30 p.m. EDT

WASHINGTON — Six of the nation’s leading LGBT rights advocacy groups on Tuesday announced they were withdrawing their support for the Employment Non-Discrimination Act (ENDA), fearing that broad religious exemptions included in the current bill could compel private companies to cite objections similar to those that prevailed in a U.S. Supreme Court ruling last week.

The withdrawal was first announced earlier Tuesday by The National Gay and Lesbian Task Force, and by mid-afternoon the American Civil Liberties Union (ACLU), Gay & Lesbian Advocates & Defenders (GLAD), Lambda Legal, the National Center for Lesbian Rights (NCLR), and the Transgender Law Center issued a joint statement that they would no longer support the current version of ENDA because it provides “religiously affiliated organizations … a blank check to engage in workplace discrimination against LGBT people.”

At issue is last week’s U.S. Supreme Court ruling in a case brought by Hobby Lobby that said family-owned businesses do not have to offer their employees contraceptive coverage that conflicts with the owners’ religious beliefs.

The ruling has since led to an increase in calls for greater permission to discriminate against LGBT Americans on the basis of religious liberty.

The action leaves the Human Rights Campaign (HRC) as the only national LGBT advocacy group to continue lobbying for the legislation in its current form.

In a joint statement, the ACLU, GLAD, Lambda Legal, the NCLR and the Transgender Law Center said their support for ENDA “is no longer tenable:”

The provision in the current version of the Employment Non-Discrimination Act (ENDA) that allows religious organizations to discriminate based on sexual orientation and gender identity has long been a source of significant concern to us. Given the types of workplace discrimination we see increasingly against LGBT people, together with the calls for greater permission to discriminate on religious grounds that followed immediately upon the Supreme Court’s decision last week in Burwell v. Hobby Lobby, it has become clear that the inclusion of this provision is no longer tenable. It would prevent ENDA from providing protections that LGBT people desperately need and would make very bad law with potential further negative effects. Therefore, we are announcing our withdrawal of support for the current version of ENDA. For decades, our organizations have challenged anti-LGBT workplace discrimination in the courts and worked for the passage of inclusive non-discrimination laws at the local, state, and federal level. We do this work because of the devastating toll workplace discrimination has had, and continues to have, on the lives of LGBT people. It is unacceptable that in the year 2014, men and women are forced to hide who they are or whom they love when they go to work. The current patchwork of legal protections at the state and local level has left LGBT people vulnerable to discrimination. For this reason, we have supported federal legislation to explicitly protect LGBT people from discrimination in the workplace, and have urged President Obama to sign an executive order banning federal contractors from discriminating on the basis of sexual orientation and gender identity or expression. […] Because opponents of LGBT equality are already misreading that decision as having broadly endorsed rights to discriminate against others, we cannot accept a bill that sanctions discrimination and declares that discrimination against LGBT people is more acceptable than other kinds of discrimination.

Earlier Tuesday, Rea Carey, executive director of the Task Force, told The Washington Post that religious exemptions in the version of ENDA passed by the Senate last year are too broadly written and would allow religious institutions or companies to fire LGBT workers, or not hire them based on religious beliefs.

“If a private company can take its own religious beliefs and say you can’t have access to certain health-care, it’s a hop, skip and a jump to an interpretation that a private company could have religious beliefs that LGBT people are not equal or somehow go against their beliefs and therefore fire them,” Carey said in an interview with The Washington Post.

“We disagree with that trend. The implications of Hobby Lobby are becoming clear,” she added.

ENDA, approved in the Senate in November 2103, would outlaw workplace discrimination against LGBT Americans, but critics say the broad religious exemptions would allow religiously-affiliated employers, hospitals, colleges, and charities, to discriminate on the basis of sexual orientation and gender identity.

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As well, ENDA does not prohibit discrimination in housing, public accommodations, education or many federal programs.

Meanwhile, House Republicans have said they will not consider the bill, in part because they believe ENDA’s current religious exemptions aren’t broad enough.

LGBT rights advocates say expanding the Civil Rights Act of 1964 to include sexual orientation and gender identity would offer comprehensive civil rights protections for LGBT Americans.

Carey said her group is also pushing to ensure that President Obama does not include a broad religious exemption in an executive order that he is expected to sign that will ban discrimination against LGBT employees of federal contractors.