WASHINGTON—After a visit to a federal detention center in Texas earlier this year, Scott Lloyd focused on the details of one pregnant girl. He wanted to ensure she had food she liked and was comfortable, and he wanted to counsel her against having an abortion.

“Often these girls start to regret abortion,” he wrote in March in a follow-up email to a subordinate. “If this comes up, we need to connect her with resources for psychological and/or religious counseling.”

The...