Several websites claim that the charity is dedicated to promoting the power of the EU, and the British National Party describes the organisation's employees as "traitors".
A statement on the BNP site reads: "The day will come when these people will have to answer for their crimes to this country."
Earlier this year, Eurosceptic Conservative MP Philip Davies wrote to the Charity Commission to question Common Purpose's charitable status (4 June, p4).
David Bell, a Common Purpose trustee, denied that it had a pro-EU agenda. "I have been closely involved with Common Purpose for more than 10 years and this is simply not the case," he said.
Another website, Stop CP, encourages readers to submit Freedom of Information requests to their local authorities to find out who has attended the charity's training courses.
A spokeswoman for Common Purpose said that the charity was concerned at the volume of FOI requests being made about it. "These appear to have the aim of causing disruption and harassment to Common Purpose as a third party, and, consequently, to the public authority itself," she said.
Common Purpose now forwards its list of 130 previous FOI requests, including names of applicants, to help local authorities decide whether new requests about the charity are vexatious.