I feel your pain, and I used to worry about damage done to Christian credibility by the Discovery Institute. It’s certainly true that the DI makes Christianity look bad. But I’m not sure that Axe’s disavowal of scientific thought, or his consistently misleading statements about science and his critics, will affect the specific credibility of “Christians in science.”
I say this because I just don’t see any attention being paid to Axe or the DI in the scientific community. He’s publishing silly papers in a vanity journal that isn’t indexed in PubMed or Scopus. Neither he nor any other DI scholar seems to attend scientific conferences or engage in even the most rudimentary interaction with the scientific community. It really does seem that the DI is solely a small group of political apologists with a platform that just doesn’t reach science. Unlike Ken Ham and his apparatus, which can make the news by virtue of bizarre spectacle, Axe and the DI are irrelevant.
They can do damage by keeping lots of people in the dark, and Christians should worry about that. But in my opinion and in my not-so-limited experience, mainstream scientists know that Christians can do good work. Axe is long gone, and so is Ken Ham, but [content removed by moderators]. Again, just my opinion.