AFAIK, in the US the only crime they could have been charged with is trespassing.
From what I can tell, it is more about foreign money(from the US) subsidizing the Civil Society NGOs in Russia.
You may recall John McCain tweeting to Putin that the Arab Spring was coming to Russia. Or, that those NGOers in Egypt were all convicted. Those American NGOers in Egypt were allowed to leave the country but were convicted in absentia.
The consensus of many around the world is that this NGO money from US AID and private sources like George Soros and others is being used to destabilize.