You must remove the tape before you paint, or before you apply new tape.
I just did mine and it was fairly easy.
Stay away from heat guns. I find they seperate the tape from it's adhesive backing, leaving behind a mess.
I let the sun do the work for me. My boat is still up on blocks with the port side facing east, and the starboard side facing west.
I took off the boot stripe tape on the port side when I got to the boat in the morning. I used a fresh safety razor blade carefully, and it came right off.
I used an adhesive remover (I forget the name) to remove any residue. I just applied the remover, let it sit for a few seconds, and wiped away the residue with the blade and a clean cloth.
It took me about 10 or 15 minutes to do the port side on my 30' Sea Ray Sundancer.
I did the starboard side mid afternoon, and had the same results.
I've done it before, and had used 3M adhesive remover. But, when I went to buy the 3M product at the local Hardware Store, they told me it was no longer sold in my state (NY), but they sold me a product that worked just as well. I can't remember the name of the product, but can get the name if anyone needs it.