The issue with being misrepresented (systemically, for ideological reasons) happens to everyone, everywhere.
I hate to bring up the Vatican again so soon, but the august Cardinal Richelieu is attributed to the following quotation:
"If you give me six lines written by the hand of the most honest of men, I will find something in them which will hang him."
This is basically the crux of your problem; and a good scientific paper contains much more than a mere six lines of text.
Consider the demographics that are normally implicated, and how they twist even their own "axiomatically true" doctrinal texts all out of context for such purposes. (I don't mean to pick on the religious conservatives, but they represent a statistically significant fraction of the demographic, and of that sample, a significant number engage in out-of-context biblical quotation bingo. It is my understanding that other conservative religious demographics have the same problem, but with their own doctrinal sources being misrepresented/interpreted for convenience of ideology.)
What is really important though, is to not lose sight of who you are ACTUALLY trying to reach; It is not the people that have already decided apriori that they need to mock, ridicule, and debase anything and everything you or your peers put on paper for the public (because they can). It is for the people that would like to know, but are being shouted at/against by the prior group, and who are kept in the dark as part of their indoctrination and cultural conditioning, but would much rather have a broader, and more meaningful understanding than just the straight diet of dogma they get at home. (if anything, the fact that these previously disparate groups have all joined up together into a siren's wail of terror, indicates that outreach is WORKING, rather than failing. They see you as competition in gaining mindshare, and have upped their game.)
Being harangued by the vocal gestalt of social idiocy is to be expected; When you get criticized by the genuinely curious young minds, that is when there is an issue.
And really, current academic publishing DOES have that issue. (See for example, the slew of really bad papers that have been getting accepted to peer reviewed journals in recent years that are literally nothing but buzzwords thrown together by a markov chain generator. 'sa truth sera.)
When you lose that demographic, you fail to replace your ranks as you age, and retire.
When you stop doing the outreach altogether, because of fear of the seething death cries of the willfully ignorant-- you guarantee the loss of the second as well.