“I keep going back to who Jesus was when he walked on earth,” she said. “This is about proximity to people in pain.”

Image Emily Mooney said that placing a “Beto for Senate’’ sticker on her car and driving it to church felt like an act of rebellion. Credit... Ilana Panich-Linsman for The New York Times

It’s far from clear how much influence voters like Ms. Clarke and her friends will have in the Senate race. Texas remains a deeply conservative state. One in three Texans is evangelical, according to the Pew Research Center, and 85 percent of white evangelical voters in Texas supported Mr. Trump in 2016, higher than even the national average, which was a record high for a presidential election. Republican strategists dismiss the notion that their Texas base shows any signs of cracking.

“It’s not worrisome at all. That would be an anomaly,” said Chris Wilson, a strategist for Mr. Cruz, citing data from his firm showing Mr. Cruz leading Mr. O’Rourke 87 percent to 11 percent among evangelical activist voters.

The New York Times’s Upshot section has been polling the race, and most public opinion polls show Mr. Cruz holding a small lead.

Still, Ms. Mooney and her friends may represent an under-the-radar web of white, evangelical women in Texas whose vote in November may be more up for grabs than at any time in the recent past. They are angry with many of Mr. Trump’s policies, and frustrated because they feel their faith has been weaponized to support his agenda.

Sarah Damoff, who is a court-appointed special advocate for children, voted a straight Republican ticket after Kermit Gosnell, a Pennsylvania physician, was indicted in 2011 for murdering babies born alive in botched abortions. But she was moved watching Mr. O’Rourke sit with migrant women separated from their children, and reflected on her own vulnerability growing up with a single mother who was blind.

“How does my vote represent the little girl that I used to be ?” she said. “The Republicans used to be the party of family, and morals and values, and now they are not.”