My memory of the stories is that it wasn't commonly known that the Second Foundation existed.
There was a single mention of it in a report of one of the first planning meetings. That mention was basically "two Foundations at opposite ends of the galaxy." Nothing more, and there were no other public mentions of it at all.
Only Ebling Mis found that mention and followed it.
The equations the Second Foundation used depended on the mass of the people acting normally. They could predict the mass reactions fairly well.
As long as the mass of the galaxy's people behave normally, everything is fine.
Some few who know of (or believe in) the existence of the Second Foundation don't (mathematically) matter.