Phases of the tactic
The tactic much resembles a con, given that it is a deceitful measure.
1. The organization first scans the internet and the websites of public schools and institutions, in addition to online newspapers and other publications searching for words such as 'nativity scene', 'pledge of allegiance', and the like. Further filters sort out these results until they are able to use staff members to find so-called 'unconstitutional activity'.
2. Second, once they have flagged 'unconstitutional activity, they report this to supervisors, who develop a case against it if they can. They find out information about the community where the 'illegal activity' has gone on.
3. Using this information, they then write a phony letter on behalf of an 'anonymous local resident'. The anonymous local resident is either an AHA member (highly unlikely, given there are only 20,000 in the contiguous United States), or an actual local resident. Most if not all times, it is the work of computer technology. (You will notice lawsuits on behalf of organizations such as these have increased dramatically over just the past 10 years.)
4. They then threaten lawsuit in these letters. The very threat of lawsuit usually scares the institutions and thus, they seize 'unconstitutional activity'.