When Gov. Asa Hutchinson, Republican of Arkansas, spoke on Wednesday about the future of what proponents call the religious freedom bill pending in his state, he disclosed that the proposal had drawn resistance from a particularly noteworthy critic: his son, Seth Hutchinson.

But to people familiar with the Hutchinsons, long one of the most influential families in Arkansas, the news was hardly a bombshell.

“It would be surprising to me if he didn’t do that,” said Shawn Standefer, a childhood friend of the younger Mr. Hutchinson who captained their national championship-winning Quiz Bowl team in high school. “He’s always been concerned with justice, however he’s thought of it.”

And so it was on Saturday, with lawmakers nearing a vote on the legislation that critics said would legalize discrimination against gay people, that the younger Mr. Hutchinson wrote to his father and warned that the proposal could damage Arkansas’s reputation and economy. It was only the latest chapter in a politically complicated relationship between Asa Hutchinson, a former congressman, and Seth Hutchinson, 31, an organizer for the Texas State Employees Union.