The Trump administration reportedly is preparing to offer job protections for health-care workers who refuse to perform abortions or to treat transgender patients because of moral objections to doing so.

News of that proposed rule broke Tuesday night, hours before White House press secretary Sarah Sanders announced that President Donald Trump on Friday will become the first sitting president ever to address the anti-abortion March for Life in Washington, D.C.

The proposed rule comes on the heels of the administration's attempts to block undocumented immigrant teenage girls in federal custody from obtaining abortions.

And the reported effort comes days after the Department of Health and Human Services either fired or accepted the resignation of a hard-line abortion opponent as head of HHS' family planning programs and replaced her with a leading skeptic of birth-control-promotion efforts.

Politico first reported Tuesday on the administration's plans for a proposed rule that would "shield health workers who refuse to perform abortions or treat transgender patients."

The news site reported that the rule also seeks to "punish organizations" that do not permit their workers to express their moral objections to providing certain medical procedures or treating certain kinds of people.

The article noted that Roger Severino, who is head of HHS' office of civil rights, "has a long record of advocating for religious groups and arguing against LGBT projections."

"Severino also has been a strong critic of providing procedures to transgender patients seeking to transition," Politico's article said.

HHS, which did not respond to Politico's request for comment on the proposed rule, did not immediately respond to CNBC's own request for comment for this story.

The Democratic National Committee blasted the proposed rule Wednesday.

"Once again, women and the LGBTQ community are under attack from the Trump-Pence administration," said DNC director of women's media Elizabeth Renda and director of LGBT media Lucas Acosta in a prepared statement. "Days before the anniversary of the Women's March, Republicans are giving health workers a license to discriminate against women and members of the LGBTQ community."

"It wasn't enough to try to strip transgender Americans of their right to serve, roll back access to birth control, and attempt to defund Planned Parenthood," they wrote. "Now Trump, Pence, and their Republican cronies want to allow health care workers to discriminate and rip away access to medical care. This rule is unethical and dangerously undermines public health."

Dr. Ben Brown, an OB-GYN in Chicago and a fellow with Physicians for Reproductive Health, said the proposed rule could have a negative effect on patients, by leading to unnecessary delays in urgent care needs.

"And that causes harm," Brown told CNBC.

The doctor said that as a Quaker, he is sensitive to the moral concerns of his fellow health-care workers.

But Brown also said, "I'm a doctor because I'm a Christian."

"While it is absolutely important to respect the diversity of beliefs among providers, our basic job is to serve these patients and meet their basic needs," he said. "Imposing one's beliefs on someone else is contrary to that value."

"The important thing is that the patients get the care that they need."

On Sunday, an undocumented teenage girl who had been in federal custody and whose desire for an abortion was being thwarted by HHS was released into the care of a sponsor.

The girl, known in court papers as "Jane Moe," was the fourth pregnant undocumented teen publicly known to have sued HHS with the assistance of the American Civil Liberties Union over a new Trump administration policy that bars federal shelters from helping women in getting an abortion.

It is not known if Jane Moe has since obtained an abortion, but the other three girls have done so.