My dropout carbon Enve fork (on a steel bike) popped out of my Yakima roof rack once a few years ago. Somehow the bike fell inward and there was no damage, but it was the last time I tried that. (No issues with that rack or its siblings in > 10 years prior with non-carbon forks.) That rack went when the minivan died, and I replaced it with a Rockymounts rack. It has a very serious and conceptually rigorous fork clamp:
(However, I asked them about it, and their reply was "never put a carbon fork in it." It is the best fork clamp I have seen, but after their warning, I haven't risked it.)
I bought a Kuat rack to go on the back of my SUV. The bike rides safely in that, as long as some CA tailgater doesn't rear-end me.