Hidalgo County, situated along the border that separates Texas and Mexico, is home to one of the country’s fastest-growing but poorest populations. Largely Hispanic and Catholic, the county also has one of the highest birth rates in a state where Medicaid finances more than half of all deliveries.

Not all of those new mothers and fathers are ready to be parents, and Patricio Gonzales, a former social worker in McAllen, the county’s largest city, has witnessed the consequences — case after case of child neglect and abuse. Convinced that family planning could be a solution, he became the chief executive of the Planned Parenthood Association of Hidalgo County, which was founded in a Methodist church in nearby Mission.

In 2010, the Hidalgo County network’s eight clinics provided family-planning services to 23,000 patients, many of whom are uninsured and cannot afford to pay. The services include contraception, breast and cervical cancer screenings, testing for sexually transmitted diseases, and wellness exams for both men and women — but not abortions.

“Basically, we are their doctors,” Mr. Gonzales said. “And for many of them, this is a way to help them get out of poverty.”