Around the rim of my Bontrager tires, which are about 6 months old, there are small thin rubber thread-like fibers coming off. The brakes do not rub. I ride a Trek 7100 on asphalt roads, with several tall hills I ride down. Do I need to replace the tires?
The word is SPRUE and can present as a short rubber "hair" 1-2 milimetres thick, or a long thin straggy line around the tyre, somewhat like a fish fin.
If your rim tyre is too narrow for your tyre then its possible for the edge of the rim to wear on the tyre. This could produce threads that really are thread, instead of rubber. I've never seen this on road tyres, but its a rare possibility on oversized MTB tyres on hybrid/cruiser rims.