I can answer this with complete certainty. AFTER the clearcoat and at least 30 days after all the paint is done. I have a 1983 Rampage 2.2. It came with factory vinyl stripes from front to back. At some point the previous owner had some minor bodywork done all on the drivers side. To help it blend in, the Paint shop clearcoated the whole side of the car over the stripes. 95% of the clearcoat on the stripes separated and peeled off leaving a car that looks like it has leprosy. The other side looks great. Don't do it!
The paint off-gasses for some time after the paint job is done, so you don't want to put the stripes on until after that process is done. The stripes are not supposed to be as glossy as paint.
IMHO the stripes like a periodic wipe down with an excellent detailers spray.
The other thing that I learned after my first set of stripes is that you hardly ever get all the bubbles out. Rather than damaging the stripes trying to work every little bit out, be patient. A good 80+ degree day in the sun, and the bubbles magically disappear.