The team were given a hostile reception at the pre-race team presentation in the west of France two weeks ago, but climbed Alpe d'Huez yesterday to a chorus of boos with boos and whistles also greeting Geraint Thomas's victory and the presentation of his yellow jersey.
"The riders of the Tour, the champions of this race, need to be respected," Christian Prudhomme, race director of the Tour de France told AFP. "I heard the whistles on Alpe d'Huez, just as I did in the Vendée.
"On the roadside it's been calm for the past 10 days or so, with very few anti-Sky or anti-Froome banners. But suddenly, we've seen a lot more.
"All I can do is renew calls for calm, for good sense and for serenity with regard to the riders on the Tour de France."
Watch: Tour de France 2018 stage 12 highlights
Prudhomme, who has been the race director since 2007, also criticised the actions of fans on Alpe d'Huez, with a number carrying flares that blew smoke into the faces of the riders, while a pinch-point in the fans combined with passing police motorbikes caused Vincenzo Nibali to crash and ultimately abandon the race.
"Some fans have only one wish: to be on television and take a selfie," Prudhomme continued. "We don't want to see that again.
"Rocket flares don't belong in bike races. They make the riders breathe in noxious air and they blind them. It just doesn't make sense.
"The vast majority of the fans on the roadside are well-meaning but yesterday, on the second half of the climb, the public were at times a little reckless."