Remove when dry.
I can understand why you might think that removing painters tape when the paint is still wet might be a good idea. After all, the tape will have no resistance. It should peel right away. Right?
A couple of issues come up, though. First, you're dealing with multiple yards of paint-laden tape, which inevitably will touch your nice, clean walls. Don't think that it won't happen, either. It will. Second, the very instant you remove the tape, wet paint may seep into your formerly taped-off area.
Blue painters tape is actually strong enough to cut through one layer of dry latex paint. You can probably even push it up to two layers of paint, but I wouldn't try for three. Pull the painters tape away quickly, but not so quickly that you rip the tape. The tape will zip right through the paint.
Yes, sometimes the tape won't zip neatly through. In this case, have a sharp utility knife or X-Acto on hand to cut the paint manually.