I suspect that being an icon gives Dolly Parton a certain amount of leeway that most artists don't get.
The fact that Dolly is iconic definitely plays a big part, but also while she has spoken out in support of groups like the LGBTQ+ and black communities and delivered messages of inclusivity, I've never particularly seen Dolly Parton as being polarizing or even "going against the grain" in that genre. While the article that radiofan2023 posted does point out some subtleties in her more mainstream music, they were just that and to Tom's point, those songs were released decades before the US became so polarized politically and before the days of 24 hour news cycles and social media which also likely helped her fly under the RADAR. Also note the article radiofan is referencing is from a website called "Country Queer" and is obviously looking at Dolly, her body of work, comments and actions from a specific perspective and through a particular lens.
When most musicians and artists find themselves and their comments being called out in the media, it's not often because of their music or lyrics, but because of comments they've made publicly, during interviews, on podcasts and the like. If you want to use the Dixie Chicks as an example since they're cited above, their real controversy started when, during a concert, Natalie Maines got on the mic and said "Just so you know, we're on the good side with y'all. We do not want this war, this violence, and we're ashamed that the President of the United States is from Texas." Lennon's "We're more popular than Jesus now" statement was made to a journalist. Dolly Parton has really never said anything particularly polarizing so far as I'm aware (unless being openly accepting of those who aren't always embraced by white Christian folk in the south can be considered "polarizing").
Lastly, Dolly has repeatedly used her wealth to fund causes she believes in, and many are either not well-known, or are cases where she hasn't drawn attention to her good works, but others have. During the worldwide pandemic, she donated $1M to Vanderbilt University for research, which ultimately resulted in the Moderna vaccine. I've seen the program mentioned on Facebook and social media where Dolly will send a free book per month to any kid 5 and under, to help support literacy; she's given money to reduce dropout rates and support higher education; given money or set up foundations and/or held benefit concerts following natural disasters, and yes, openly supports the black and LGBTQ+ communities. In other words, she's definitely done a lot of good in many ways, without being particularly controversial or polarizing.