That polling company is known to have asked loaded questions in polls and the accuracy record appears to vary. I'm not sure if it reflects reality or fear, because in general, less than 50% of the population become alienated to fully embrace anti-reality disinformation... Also, there is a difference with accepting the possibility that one in a million may suffer from strong immune reactions (fact), and believing that the vaccine is dangerous to most people (lie and alienation, forgetting the actual purpose of vaccines and denying their efficacy, etc.)
Edit/Adding, as for the 1/4 believing someone they know died because of the vaccine, it's clearly a false belief that does not match the actual data. Any cause of death, including SARS-CoV-2, could be misconstrued. Just like vaccines have been falsely blamed for the usual causes of death. Why believe incompetent random people's stories? It's part of the scientific method to avoid that kind of mistake.
Edit/Adding 2, some interesting links:
https://web.archive.org/web/20120508102347/http://www.washingtonpost.com/wp-dyn/content/article/2010/06/16/AR2010061605090_pf.html
https://web.archive.org/web/20230322072843/https://www.washingtonpost.com/media/2023/02/28/rasmussen-poll-scott-adams-dilbert/
https://web.archive.org/web/20230317212246/https://www.washingtonpost.com/politics/2023/03/17/arizona-election-kari-lake-rasmussen-poll/
https://web.archive.org/web/20221202062953/https://www.dailykos.com/stories/2010/5/19/867829/-Rasmussens-%28dishonest%29-game
https://web.archive.org/web/20120731004315/http://www.tnr.com:80/blog/jonathan-chait/75161/the-rasmussen-problem
https://web.archive.org/web/20160820125323/http://www.pollster.com/blogs/a_question_thats_too_salty.html
https://web.archive.org/web/20120602163552/http://www.politico.com/news/stories/1209/31047_Page3.html
Edit/Adding 3:
So ad populum fallacy using fabricated results obtained with misleading suggestive zone flooding, loaded questions asked to select demographics, and then quote mining the "polls" that showed the "results" they hoped to obtain, promoted with the intended twist, to amplify falsehoods and the impression of their acceptance, increasing radicalization. It reminds me of the Mind Maker in Attack of the Killer Tomatoes...