My white handlebar tape is an absolute nightmare to keep clean even using Sprint Spitfire Spray and I don't have time in my life to keep on top of it. Are there any bar tapes out there that are very easy to maintain? The tape does not necessarily have to be white.
The secret with Handlebar cleaning and also with brake hoods (I have white ones, it's cool but it never stay clean more than 10minutes ^^) is to use some hospital-grade ammonia based cleaning products.
Since your stains are essentially composed of handfat and dirt you will clean your tape with minimal effort.
Ease of cleaning and maintaining appearance is one of the things shellacked cotton has going for it the strongest.
With shellacked tape, what wears primarily is the dried shellac matrix. You have to let it go a long time before the actual tape material is exposed.
To clean it you just put some alcohol on a rag and wipe it down, which quickly makes it look good as new unless it's getting worn down. And then to replenish it you mix up more shellac solution in the same alcohol and re-apply some layers.
You can keep the same tape going a very, very long time this way, always looking good.
For cleanable conventional/modern tape options, the best I've seen are Lizardskins DSP and Fizik Superlight Classic, which both wipe more or less clean with alcohol.