"These campaigns against our partners are generally orchestrated by animal rights organizations whose views are extreme and entirely out of step with U.S. public opinion," said SeaWorld spokesman Fred Jacobs, who calls them a form of "digital harassment."
"We do not have any plans at this time to remove the Barbie I Can Be SeaWorld line from our stores," said Kathleen Waugh, vice president of corporate communications for Toys R Us. Groupon declined to comment for this story.
(Read more: PETA protests injury to whale at SeaWorld San Diego)
SeaWorld defends its practices and, in a variety of public statements, accuses the "Blackfish" film producers of painting "a distorted picture that withholds from viewers key facts about SeaWorld—among them, that SeaWorld is one of the world's most respected zoological institutions, that SeaWorld rescues, rehabilitates and returns to the wild hundreds of wild animals every year and that SeaWorld commits millions of dollars annually to conservation and scientific research."
Still, citing the "Blackfish" documentary and petitions signed by fans, performers such as Martina McBride, 38 Special, REO Speedwagon, Cheap Trick, Trisha Yearwood, Heart and Willie Nelson have canceled their events at SeaWorld venues.
"I understand there are petitions going around with thousands of people's names on it, so I had to cancel," Nelson said in a CNN interview. "Also, I don't agree with the way they treat their animals, so it wasn't that hard a deal for me to cancel."
For other performers and companies being urged to cut ties with SeaWorld, the decision may not be as easy, said Shailendra Jain, chair of the department of marketing and international business at the Foster School of Business at the University of Washington in Seattle.
Some may choose to encourage dialoge "to get to the bottom of the matter," said Jain. Others may need to "examine analytically the costs and benefits of discontinuing SeaWorld as a co-brand," staying with them for the long run or, in the short run, adopting a "wait and watch stand—as Southwest is doing," he said.