* Un-tasteful: Meaning not tasteful, lacking good taste.
* Over-tasteful: Meaning excessively tasteful, perhaps to the point of being pretentious.
* Pre-tasteful: Meaning having good taste in advance, or showing good taste in advance of something.
You could also create more abstract prefixes, like:
* Hyper-tasteful: Meaning extremely tasteful.
* Neo-tasteful: Meaning having a modern or innovative sense of taste.
Ultimately, the best prefix to use will depend on the specific context and the desired meaning.