Washington (CNN) A broad coalition of women's reproductive rights groups and LGBT health organizations is asking a court to strike down a new rule issued by Trump administration that excuses religious and moral objectors from participating in or paying for services such as abortion, sterilization and assisted suicide.

In a complaint filed Tuesday , the groups argue that if the rule were to go into effect, it would "encourage health care workers to deny medical treatment to patients because of personal religious or moral beliefs."

"The rule is intentionally unworkable for health care facilities, including hospitals, and may result in these facilities doing away with reproductive and LGBTQ services altogether to avoid losing government funding," legal groups representing the plaintiffs said in a statement.

The Center for Reproductive Rights, Lambda Legal and Americans United for Separation of Church and State are among the groups representing several LGBT and women's clinics named in the case. Other plaintiffs include California's Santa Clara County and the Association of LGBTQ+ Psychiatrists.

Richard B. Katskee, legal director for Americans United for Separation of Church and State, said the rule was "unconstitutional in at least four ways" -- including violating the Equal Protection Clause by targeting marginalized communities.

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