The issue, and the principle at stake, has put abortion rights supporters in the unusual position of opposing Medicaid funding for family planning services.

The Texas program, now called Healthy Texas Women, provides contraception and screenings for cancer, H.I.V. and sexually transmitted diseases, and as of last year, screening and treatment for diabetes, high cholesterol and high blood pressure, to women ages 15 to 44, with income up to 200 percent of the poverty level — about $23,760 for an individual — who do not qualify for Medicaid. It used to be what is known as a Medicaid waiver program, financed 90 percent by the federal government and 10 percent by the state. About half the states have similar programs for low-income women not otherwise eligible for Medicaid, Ms. Nash said.

But Texas turned its version into an entirely state-financed program in 2013, when it cut out providers that “perform or promote elective abortions,” or contract or affiliate with providers that do so.

Other states have recently expressed a willingness to forfeit Medicaid funds if doing so allows them to block Planned Parenthood from receiving tax dollars. This year, Missouri ended its Medicaid waiver program for family planning services and instead set up a state-financed program that excludes abortion providers. Iowa is planning to do the same.

The reduced funding in Texas has led to a drop in women receiving services through the program. The Texas program had an average monthly enrollment of about 79,000 last year, according to the state, down from 126,000 before it cut out Planned Parenthood and other abortion providers. In the first 18 months after the change — which resulted in a loss of $35 million a year in federal Medicaid funds — thousands of women stopped getting long-acting birth control, and Medicaid pregnancies increased by 27 percent, according to a research paper published last year in The New England Journal of Medicine.