You're right, you can't hide from data mining. But you can confuse, dilute, and in other ways make the data collected about you less useful and more error ridden....Perhaps it is better to hide in plain sight - that is why I just use my real name and post a handle beside my real name here. - Everything we say and do is known.
A lot of crappy data is worse than no data. When you fill things out, change your middle initial now and then. It will create a new version of yourself in the data mining world.
Lose your merchant rewards cards and get new ones, using a different name or leave the identity blank.
Just mess with them. Constantly. Make it a habit. It's kind of fun to think up new ways.