"When you "protest" your image is up for grabs---be it government or the ACLU, etc. It's a risk you take, knowingly."
Isn't that the idea? To let people know that you're unhappy about something, and are willing to risk repercussions for speaking out? If you're not willing to be known in a public way, then why bother?
And the protesters, at least those who understand protest, would love nothing better than to clog up the government with work in as they prosecute / persecute the protestors. They know that if the government finds it more expensive to repress the protesters than to address the grievance then the grievance might be addressed.
Finally, there are always the psychotic nut cases who need to be violent and destructive. Those people really do need to be put in jail.
The ACLU doesn't have access to your tax records, FBI files, military records, telephone records, or computer accounts. The government does.