Greta Thunberg has Asperger’s syndrome, a condition that is akin to high-functioning autism, she also suffers from obsessive-compulsive disorder (OCD), and selective mutism. 
This, combined with her age, has blunted many of the attacks against her.
On a Fox News panel show, Buck Sexton, a guest, was scolded for “kid-bashing” after he went after Thunberg on air. 
Similarly, when Daily Wire’s Michael Knowles referred to her as a “mentally ill Swedish child”, Fox was quick to issue an apology and condemn Knowles’ attack. 
Greta’s disability, as well as her age, have created the perfect confluence of personal characteristics to deflect the right’s attacks. She refers to herself as an “uneducated teenager” and cannot be reasonably expected to defend herself against personal attacks against her values.
Additionally, those that are advising Greta have given her valuable information. She always stops short of recommending individual policies. This prevents the right from dismissing her as a member of the radical far left and framing her climate change message as a right vs left, liberal vs conservative, capitalist vs socialist matter. She has not publicly endorsed policies like the Green New Deal. Instead, she simply urges people to look at the science behind the issue.
In lieu of testifying to the US House of Representatives, she attached a note to the IPCC’s scientific report on limiting global warming to 1.5 degrees. 
By not being drawn into a policy discussion and deferring to the science where possible, she sidesteps many of the traditional political attacks that are often brought against climate activists.