I have the stock Dunlop tires on my nightster and it seems to get REAL squirrely when going over most painted surfaces. Mainly when lane splitting here in CA and riding on top of the double yellow lines. I see other bikes doing it all the time and doesnt look like they have any issues. It gets pretty scary at times. My guess is its the Dunlop tires. Im thinking of getting Avon venoms instead. Has anyone had this experience and did switching tires help solve the wobble?
The painted lines in roads are slippery under the best conditions. Worse when wet, or covered with oil. The vinyl lay down pieces are even worse. Best to avoid entirely. I wouldn't think one brand of tire would work better than another, but worn tires are definitely going to be a more serious situation. You should be able to roll safely over just about anything flat in the roadway. Braking, accelerating and turning (in that order) are the most likely to put you on your ***.
If you truly are a newer rider, go test ride a dyna or softail under the same conditions. JMHO but I think you need to be a damn good rider to handle a sportster on the freeway.