While she's not as big of a voice as she once was, she unfortunately still is given time to speak, mostly just for TV ratings and clicks on online stories.
I encounter vaccine hesitancy issues a lot in my current job in public health, and a lot of the current knowledge points toward vaccine hesitant parents not feeling confident talking to medical/health professionals (for a plethora of reasons). They see her as [somehow] more relatable--a fellow mother who is open to listening to concerns about vaccines (nevermind the fact that many physicians are also parents). Obviously this is the wrong voice for these parents to end up listening to, and thankfully very few actually do, but I think that's where a lot of it stems from.
She's also very charismatic, and is generally better at garnering attention than your average science-minded person. Profanity and absolutes get more hits than calmly delivered science that often comes with caveats.