Some of the country's leading secularists and agnostics have joined forces with a group of conservative Christians to defend free speech.
They fear the "writing could be on the wall" for free speech if the orders go ahead.
Christian Institute director Colin Hart and NSS chief executive Keith Porteous Wood said the legislation could inadvertently turn millions of ordinary citizens into potential extremists overnight.
"The vital importance of free speech is an issue on which both our organisations have always agreed," they said.
"We have previously been able to see off an attempt to make it illegal to be 'annoying' in public. We have prevented prosecutions for mere 'insults' by helping to secure changes to Section 5 of the Public Order Act. Extremism Disruption Orders are as bad as anything we have seen in the past – probably worse. It is another attempt by a Government to clamp down on free speech in the guise of combating extremism."
Hart added: "Every time ministers talk about extremism they seem to want to go much wider than tackling terrorists and their sympathisers.
"Law-abiding citizens, such as Christians, could be caught by the vague definitions of extremism that get bandied about when ministers are trying to talk tough.
"Broad-brush counter-extremism policies catch ordinary citizens and are actually a waste of resources. They do not make us safer. They make us less safe by distracting the authorities from focusing on genuine threats."
Porteous-Wood said: "Political activists, environmental campaigners, as well as groups like ours, could all be branded 'extremists' under the Government's massively broad proposals.
"There are already extensive anti-extremist powers available to the authorities, but they are not being fully used. The law already protects against incitement, harassment and violence."
Both organisations are founder members of the campaign Defend Free Speech created to oppose the introduction of Extremism Disruption Orders, announced by Home Secretary Theresa May in September last year. The orders would be triggered by "harmful activities of extremist individuals who spread hate but do not break laws".
Prime Minister David Cameron told the National Security Council in May: "For too long, we have been a passively tolerant society, saying to our citizens, 'As long as you obey the law, we will leave you alone'. This government will conclusively turn the page on this failed approach."