score:3
The standard reference for prohibited items in the US is https://www.tsa.gov/travel/security-screening/whatcanibring/.
Golf club shafts are not mentioned specifically. However, other similar long thin items of sports equipment such as hiking poles, pool cues, ski poles and tent poles are mentioned as not allowed in carry-on luggage. So my guess is that golf club shafts would not be allowed either.
The page suggests that you can also ask TSA directly via Twitter or Facebook Messenger. If you do, please post another answer here and report what they say.