You are wrong in several aspects of what you have written.
First, there is no such thing as a Darwinist. That's a derogatory, and false, term used by some folks in an attempt to demonize those who disagree with them. You might as well complain about Newtonists, Galileoists, or Einsteinists.
Second, when some folks make claims that contradict what science has found, it is only natural for science to examine the evidence in terms of those claims--and to examine those claims in terms of scientific evidence. The claim of a young earth has not withstood that examination. Now, you can believe what you want but when you make a claim that can be examined by science, don't complain when science examines that claim. And if the claim is found wanting, don't complain about being "tripped up." Rather, examine the evidence supporting your claim.
But you are right in your final comment; if you make claims that can easily be disproved, other claims you make are certainly less credible. St. Augustine noted this centuries ago:
Now it is a disgraceful and dangerous thing for an infidel to hear a Christian, presumably giving the meaning of Holy Scripture, talking nonsense on these topics; and we should take all means to prevent such an embarrassing situation, in which people show up vast ignorance in a Christian and laugh it to scorn.