I agree with you that there influence is mainly limited in terms of direct control over science, the YEC crowd does affect science through other methods.
- Incredibly opportunity loss (the disparaging of science and the negative cultural context and constant friction between groups) affects millions of people
(I teach science and math at a conservative Christian school and this dynamic does not change that much as time goes on)
- Allegiance of many YEC communities with conservative politics (in Canada, the last conservative prime minister controlled scientists ability to publicize, discuss, and present findings (“protecting intellectual property”), significantly cut some environmental branches funding and destroyed some research papers…). I can imagine at least to some extant, this occurs in the US as well.
Anti-science positions can directly and indirectly affect the process of science. It may be limiting funding to an extent (different priorities) to any other measure.
Ultimately, the social cost is incredible for people in these communities and for society in general.