I'm just wondering how it passes First Amendment muster. Also, what does "influencing" mean? It sounds like the thing they use to stop people passing out FIJA fliers.
I suspect that it is the law they use to stop people passing out FIJA fliers (in those jurisdictions that don't have laws specifically have laws recognizing Nullification, as some states do).
It is generally the case that provisions of the 1st Amendment are not held to immunize actions that would fall under criminal statutes if conducted by different means. There are other sections that cover other means of attempting to improperly affecting various officials and witnesses, and are usually stronger in their wording.
"Influencing" is usually pretty obvious from what the demonstrators are saying, doing, and have put on their signs. Note that even violence doesn't seem to get this law actually applied, even in instances when it is quite clear what the rioters are trying to do, as is usually the case when BAMN riots outside a court hearing.