The female bear, JJ4, killed 26-year-old trail runner Andrea Papi on April 5, the first Italian to be killed by a bear in modern times.
He is thought to have run into her on a trail and she reacted while protecting her three cubs.
It is still to be decided if she will be euthanised or just placed into captivity somewhere.
The new hashtag was coined against Trento Provincial President Maurizo Fugatti of the right-wing League party who has called for JJ4 to be eliminated as there is a risk she may kill again.
Many of those posting said they won't vacation in Trentino again and came out strongly against JJ4's being put down.
“I will never again go to Trentino or to any of the areas run by the League,” wrote social media user, Roberto.
“It's horrible, we have to get her out as soon as possible, moving her to the place that has been found for her, possibly with her cubs; and never again holidays in Trentino,” commented Sara, referring to a haven animal rights group LAV have found for JJ4.
Francesca said, with a weeping face emoji, “the bear has been captured and separated from her cubs, why so much cruelty?”
Ipazia wrote “enough with the witch hunts by these inadequate politician”.
“Stop massacring Trentino bears”.
Roby tweeted “Do you really want to find yourselves in the middle of these people? Their hotels must be left empty”.
Stefano said “She only did what every parent does. Defending her territory and her cubs. The woods belong to the bears. The ocean is for sharks. Mountains are for avalanches. The city is for human animals”.
WWF Italia said “someone should explain to the president of the autonomous province of Trento that there is not an electoral campaign between the bear party and the anti-bear party”.
“When he speaks about the bear JJ4 he is talking about a living being and not an object.
“The tap of propaganda on the management of bears in Trentino must be turned off.”
Other animal rights groups said they would defend JJ4 “in all the ways that we are allowed to”.
Paolo Colangelo of the National Research Council (CNR) said “bears only become aggressive when they feel threatened”, adding that “in Trentino they have lost the culture of cohabiting with the animals”.
The bear population in Trentino has boomed to around 120 after the start of a campaign to stop them dying out at the turn of the millennium.
Other countries including Romania and Slovenia are implementing culls to curb growing bear populations.
ANSA