Some NGOs say they fear the law will be used as a tool of repression against anti-government groups.
Thai lawmaker Panich Vikitsreth and Narumol Jitrawarattana, were released after they paid their bail, approximately at $250 each.
The seven Thais, including a member of parliament, are facing a potential prison sentence of 18 months, for illegal entry into Cambodia.
Hun Hean was removed from his post following the January 7 holiday celebrations.
Jan. 7 remains a contentious day for Cambodians, marking both the ouster of the Khmer Rouge and the beginning of Vietnamese occupation.
Critics say the proposed law creates tangles of red tape that could be used to attack groups that don't follow the government line.
Relatives of the defendants, reporters and Thai Embassy officials were barred from the courtroom in Phnom Penh on Thursday.
The seven suspects, including a Thai member of parliament, were detained last week for allegedly crossing the border illegally.
Residents say they will sit at Freedom Park, for a week in search of mediation.
The law will require NGOs to provide financial reports and action plans to the government.
According to reports, the defendants were on a fact-finding mission investigating Thai claims of Cambodian border encroachment.