To answer your question, it doesn't have to be blue tape!
To be honest, tape is not my favorite bed adhesion solution, there are plenty other options that work better than tape.
Often you'll see references to blue painters tape (of a certain brand) to be used as a bed adhesion layer because many people have good experience with that. I have tried several tapes, white/cream to blue from various vendors but found that neither of the tapes satisfied my personal needs. To name a few: cleaning, application, preparation, repair, tear-off, no glossy first layer, color of tape sticking to printed part, etc. did not make tape a favorite bed adhesion solution. Instead I've been printing directly onto aluminium and glass using an adhesive (3DLAC or DimaFix) to stick filament to the bed. Use a wet cloth to wipe residue off, spray can to apply a new layer, et voila, just print, it always sticks! Glue stick is also a possibility.
So while the community screams "use blue tape", you just cannot use any blue tape from any tape manufacturer. There is no standard to which blue tape has to comply. Generally, speaking from painting experience, many blue tapes release much more easily after use while the white/cream paper tape sticks better and often tears (but this is frequently the tape that is already applied on heated beds of many Chinese printer kits, see image above). Not all tapes are equal: I have used blue tape from a local cheap source that will not stick to the build plate when it heats up, even if properly cleaned.
I'm more inclined to think that the color of the tape is just a way to distinguish yourself from the market back when the first manufacturer introduced the tape. Now that it is more common, others have adopted the color mimicking the tape they want to copy. It is more about the adhesive than it is about the surface of the tape (as in: "tape is rougher than the substrate you stick it on"), also you read that many people using blue tape need to prepare it by cleaning it (remove waxy layer) and sanding it.
IMHO, you just need to experiment yourself with several solutions and see what works best for you, could be that the white/cream tape from a local source also does the job. So basically, your tape does not have to be blue, it has to work!