I use a roof rack and it's never been a problem. As others have said, there's aluminum reinforcement, so it's fine. I also think it's the best looking way to carry a bike. lol
Road bikes are light and it's really not a problem but even my heavier mountain bike is fine.
Just be aware that your gas consumption will take a small hit do to the wind resistance.
With the mountain bike you can see the adapter someone mentioned before, for thru axles (15mm in my case).
