rebdoniel,
The things you list are not equal. I do not think it is fair to say that frum people reject scientific and public health evidence
1) Vaccinations: I have never heard of any Rabbi or any Frum person of prominence who has claimed that people should not vaccinate their children.
2) Brain Stem death: This is a halachic machlokes about what constitutes death, not a scientific one.
3) Abortion: the status of a fetus in its mother’s womb is a Machlokes Rishonim (Rashi v. Rambam) and has been the subject of debate within halacha since that time. It has nothing to do with a rejection of science (if anything the science is on the anti-abortion side).
4) The evidence on homosexuality is mixed. Both sides pick and choose what evidence they use.