I would like to not earn reputation, but still participate in this site. Is that possible? Why or why not?
The only way you could participate in the site without changing your reputation would be making useful comments on other people's posts. Theoretically, you could achieve this by making every post you make community wiki, but that would be abusive behavior and would probably get you suspended.
Reputation is a measurement of how much the community as a whole trusts you. We cannot simply allow an individual to prevent the community from making that measurement.