So I went through this exercise years ago, I installed lots of trim in my house and painted with colors so cutting in would be very time consuming and stressful. In fact with base or chair rail its nearly impossible to cut in when painting wall after trim - I had a pro tell me in this case they paint the wall first, then chair rail, then wall under chair rail then base (top to bottom method). The problem with painters tape is that its designed primarily for easy releease so its made from crepe paper - thus no chance of blocking seepage.

There are tapes made from smooth almost plastic like backing at the home centers (Scotch). The one I used is also blue and I just looked it up, seems they may have changed the name from what I have, now they call it sharp lines. This will make a huge difference as long as the surface you are taping to is perfectly clean and not too textured.

I tried the Frog tape once and spent hours applying it and next morning it had all fallen off, I think the adhesion is really low.