On paper, Matt Beebe and Steve Allison — the GOP candidates in a runoff for Texas House Speaker Joe Straus’ open seat — would seem to align on the issue of gun rights.

Both are members of the National Rifle Association. Both boast A-ratings from the organization. And both consider themselves strict constructionists and strong supporters of the Second Amendment.

But a brewing clash between gun rights activists and police in Olmos Park has revealed a subtle contrast between the two Republicans that befits their respective footing in the Texas GOP.

Allison, a longtime friend of Straus, believes police have a right to order anyone who is openly carrying a gun in public to produce a license for the firearm. Beebe, a tea-party backed conservative who twice opposed Straus in the primary, sees that as a violation of the Constitution. (In Texas, licenses are required for handguns but not long guns.)

“I do think (police) have a right to ask to see a license where there’s a weapon involved,” Allison said on Friday. “Particularly with the increased concern over school shootings and terrorism, I think the police have to have the right to protect themselves and us.”

Beebe disagreed.

“That is not what our Constitution says, and I absolutely support the constitutional view that we are not to be subject to search and seizure when all we are doing is carrying out lawful acts,” he said. “Unless you suspect me of a crime … you’re starting to breach those Fourth Amendment rights that I have.”

The debate is not merely of philosophical interest. In recent days, tensions between activists and police reached a boiling point in Olmos Park, a bedroom community just north of downtown that marks the southwestern end of Straus’ district.

Last week, Olmos Park police tased and arrested CJ Grisham, president and co-founder of Open Carry Texas, at a small gun rights demonstration on McCullough Avenue. In a video of the incident, Olmos Park Police Chief Rene Valenciano is seen approaching the demonstrators and ordering them to “get on the ground,” a request they refuse.

“Do you have a license to carry a gun?” Valenciano asks.

“He doesn’t need a license to carry a rifle,” an activist responds.

“You’re interfering with the duties right now,” an officer says, prompting the activist to retort: “You have no duty to disarm a law-abiding citizen.”

From there, the video disintegrates into a blur of cursing and shouting. Grisham was charged with assault of a police officer, interfering with the duties of a public servant and obstructing a roadway. Two other activists also were arrested.

Those arrests have spawned a much larger rally scheduled for noon on Saturday. More than 100 activists, most toting firearms, are expected to converge at Melrose Place and Howard Street and march to Olmos Park City Hall.

“We anticipate that there will be some people carrying long guns — rifles or shotguns,” said Rick Briscoe, a member of Open Carry Texas. “There very probably will be some people carrying handguns with a license to carry handguns.”

Briscoe likened the open carrying of firearms to “walking down the street smoking a cigar with a cell phone in your hand.” He said participants will be protesting “the violent conduct” of the Olmos Park Police Department and calling for Valenciano to “be relieved.”

“Our intention is to conduct a peaceful, lawful event, present a petition to the city government and go home,” he said. “We expect cooperation from the Olmos Park police to allow this peaceful, lawful event to be conducted without interruption.”

Beebe stressed that the protesters will be exercising their constitutional rights. But even he was wary of this particular exercise.

“It’s not necessarily the wisest approach,” he said. “Two guys that were lawfully exercising their rights spent a night in jail, and one of them got tased. Both had concussions. In that respect, it’s hard to argue that that worked out well for anyone.”

Allison acknowledged the right to carry guns openly at the rally, as long as protestors recognize “public safety concerns,” he said, and the right of police to see licenses.

Beebe bristled at that.

“What Steve is asking for is a new class of abridged rights, a new justification for abridged rights,” he said. “I’m uncomfortable with that approach.”