I don't like the science-bro movement, but I also think they might fill an important niche. The anti-science movement has too many people and too much time and too high of a (answer time / question time) gish-gallop ratio for scientists to possibly engage with. If scientists try to fight the anti-science crowd, they will lose.
Science bros, for all their faults, can trade blows on more even footing, and that's something. Perhaps even a vitally important something. Even if science bros aren't great at science proper, their contribution to societal consensus formation might be as important as the underlying science itself!
Science bros often misuse "anti-science" to try to shutdown opinions they disagree with. Hence people worried about the unlikely event of being killed by a nuclear power plant are anti-science, but people worried about the even more unlikely event of being killed by a super intelligent AI aren't. Misusing the word "science" (particularly by people who don't seem to have a good grasp on it) and turning it into a rhetorical cudgel is harmful, and pushes the idea that science is ideological.
Science bros, for all their faults, can trade blows on more even footing, and that's something. Perhaps even a vitally important something. Even if science bros aren't great at science proper, their contribution to societal consensus formation might be as important as the underlying science itself!