Perhaps, and I'm not saying that every single person, upon hearing "neo", is going to think hardcore conservative. But most will, as there aren't many other places that that term is used, politically. Neo-liberals? Neo-revolutionary? Neo-...? Outside of politics that word is used for a lot of different stuff, but adding it to the front of "-confederate" when talking about politics... can't say I recommend it if you don't want to be associated with the big "neo-" group.
New mean new. Most Americans think it means new, the name of someone on The Matrix, or both. It is used for a variety of things. In America, some highly political people use it to refer to big government Republicans. In Germany, it is often combined with nazi.
Overall, I doubt more than a small percentage of the Americans population would thing of the word as a negative thing. Maybe more in German.
If you think most people know that Neo means New, I think you may have overestimated the average persons intelligence. It's never used in conversation, in newspapers, or on ESPN. It's just not a common enough term.