Mineral spirits will not change the color of the wood. It darkens it when wet, but when it dries the wood retains it's original tones. Blue tape sticks much greater than green painters tape, which is my favorite if I can find it. Yellow painters tape is for delicate surfaces, therefore it has less adhesive so it's lubricating properties are less than blue or green painters tape. I'm planning to experiment with adhesive backed shelf paper; I've read about some scrollers that are using it, and find it's cost and labor effective. Apply it to the wood, then the pattern over it. They say it peals off very easily.
Trust me. Plywood and tape do not mix. Even the shelf liner that some people use will lift fibers. Mineral spirits will maybe darken it a shade but no more then that. The other plus is since wipe on poly is mineral spirit based you can apply the first cost of poly before it dries.
There is another good reason to not use painters tape. I like to make the wood grain work for me. You know things like knots and swirls in the grain postitioned correctly can really make or break the appearance of a project. For this reason I trim my patterns to a bare minimum (no pun here) and I position dry on bare wood (again no nun) until I get the effect I want and then I glue the pattern down.