After a brief testing phase, American Airlines in August formally expanded the availability of unrestricted Internet access on some longer, nonstop flights.
But the Association of Professional Flight Attendants worries that letting passengers look at any website online, including adult sites, might actually endanger passengers.
The APFA's Frank Bastion said that fights might break out among passengers over adult content.
"Our members are telling us that they're concerned about [this problem]," he said. "There are certainly enough pressures in the airplane already. We just don't want one thing to add to it."
An NBC news affiliate in Dallas asked several travelers if they supported the union's stance, and most, if not all of them said they would want to have some kind of control over what appears on their computers screens.
To that end, the APFA wants to install filters that would enable passengers to block adult websites, according to KXAS News in Dallas/Ft. Worth.
But American Airlines isn't going to comply just yet. When the company unveiled the expanded Internet access, it anticipated complaints about allowing porn on board. At the time, company representatives said they would ask flight attendants to deal with misbehavior on board as they always have: by asking passengers to move to a different seat or to put away the offending material.
American Airlines stood by that policy today while also extolling the virtues of its passengers.
"We always hope our customers will use good judgment on what they view while on board our aircrafts," American Airline’s Tim Smith said. "And the vast majority do just that."
Passengers pay $12.95 to use the Wi-Fi service, which for now is only available on certain flights connecting New York to Los Angeles, San Francisco and Miami. Only flights using Boeing 767-200 aircraft will have the service.