The Council for Civil Liberties is challenging a claim by former National Party leader Simon Bridges that people should have total freedom of expression on Twitter.
Proponents of free speech are concerned at Twitter's abrupt suspension of tens of thousands of accounts in recent days, which has now reached New Zealand.
They say many of these accounts were allowed to flourish for years and the swift change in approach has not been fairly applied.
But Twitter says: "Given the violent events in Washington, DC, and increased risk of harm, we began permanently suspending thousands of accounts that were primarily dedicated to sharing QAnon content."
Last night, Bridges tweeted: "The suspension of NZ Twitter accounts is an overreaction. This isn't about whether anyone agrees with what any user was saying. It's about freedom of speech. And pushing views underground is more dangerous than letting them be out in the open for all to see."
Chairman at the New Zealand Council for Civil Liberties, Thomas Beagle, told RNZ's Morning Report that he didn't entirely agree with Bridges' view that harmful ideas should be out in the open.
Beagle said there was a difference between harmful ideas and harassment and threats of violence.
"I don't think anyone thinks that we should be able to threaten violence online and I think we do have to look at ways of suppressing harassment.
"The thing about freedom of expression is that it's not just about what people say - it's also about the ability to go and participate in those discussions.
"What we have seen in the last few years [is that] there is actually concerted efforts driven by bots and the rest to actually stop certain sorts of people having certain points of view just by harassing them into silence."
Beagle said it was also hard to say if New Zealand Twitter accounts, including people pushing conspiracy theories and far right ideas, should have been allowed to remain on the platform.
Although Twitter should have the right to remove some accounts, he would favour more transparency about who they were getting rid of and what those people had been saying.
They could also be given the right to appeal "because Twitter doesn't have a good history of actually making good decisions on these matters".
Many have been watching speech on the internet in the past few years and concluding it has gone in unexpected directions, but it was also important to consider what consistency people would see in the future now that Twitter has made this significant change "in the same way that we saw with Facebook and their similar purges of people".