Extreme right groups, shunned by payment processors and traditional companies, are turning to new methods to solicit donations.

"We can't trust these companies because these companies are all controlled by the left. We need to build own systems, our own shadow economy," Pax Dickinson, founder of Counter.Fund, told CNBC.

The site, which Dickinson says launches next month, describes itself as "an ideological crowdfunding platform and self-governing political party" operated now primarily by volunteers.

"Most of our best people are anonymous. They have too much to lose because there's no shadow economy to support them," he said.

The site will be a "grass-roots movement" where supporters can make monthly donations anonymously to a particular cause. Dickinson likened it to a "crowdfunding collective … like a grocery store co-op owned by the people who shop there, managed by the people raising money for it. The more you raise, the more likely you will be elected to the House of Lords, which is the leadership group."

He said he will handle the credit card processing himself because he doesn't trust PayPal and similar companies, and will accept bitcoin donations.

Dickinson, who co-founded the crowdfunding site WeSearchr, was the chief technology officer of Business Insider until he was forced out in 2013 after a Gawker article disclosed a series of offensive tweets he had written.