A current NC person chiming in here.
There are definitely isolated pockets that are more progressive - but as soon as you get outside of them, the culture shock is real. I live in CH. I used to live in Durham. In town, it's mostly OK. I think for day to day cycling (except a very small core in the center of CH), Durham is actually better for biking now. Chapel Hill has won all sorts of awards, but my bike commute sucks (and that's not really unusual). There just aren't safe connectors from some parts of town to other parts of town. Carrboro is better, but very small. Once you get out into the country (where you would do long rides), there is a lot of cyclist hate. Someone told me (though I haven't been able to verify it) that a pace line was shot with pepper spray recently. My DH was hit by a car last week in Wrightsville Beach, NC. On another forum I frequent, a poster was hit on the same day in Greensboro, NC (and the driver was planning to leave the scene). There's a group in the rural areas outside Chapel Hill that absolutely hates cyclists and have been working on advocacy to keep bikes off the road (Schley Grange).
TL; DR: After I finish medical school (residency at the latest), we plan to get the heck out of NC. There's just too much cyclist hate in addition to other hate (HB2, anyone?).
Most days in life don't stand out, But life's about those days that will...