It's authorized by law.
>> solely for the purpose of monitoring activities protected by the First Amendment
They don't look into such things randomly. They have some notion, say a report from someone, and examine the speech. A typical example might be some kid reporting "terrorist speech" in a public forum. So some officer somewhere takes a look, finds nothing illegal, and that's the end of things. That is an "investigation" of 1st-amendment speech because the officer is reading and investigating legal speech, but the purpose of the investigation was non-protected terror speech, or child porn, or threats, or any number of categories of illegal speech. It's not proper to turn around and call those investigations illlegal simply because they didn't find anything. That would only encourage officers to find things, to make mountains out of molehills, to justify their investigation.