NZR investigated claims that members of the Chiefs rugby team inappropriately touched, licked and threw alcohol and gravel at a stripper known as Scarlette during "Mad Monday" celebrations after their season ended.
The players have been given a formal warning which will sit as a "black mark" on their records.
The inquiry concluded that while the performance was legal and consensual, it was wrong for professional rugby teams to engage in such events and said players had to take collective responsibility.
The letter issued yesterday said the investigation "has highlighted to all New Zealanders that NZ Rugby's judiciary process is not appropriate for dealing with issues of integrity, mana, respect and basic personal rights".
Blue said it was time for NZR to address its "internal culture issues".
"NZ Rugby has previously refused to take up offers of support and expertise from external parties with these sorts of investigations. Until they do, these investigations will continue to produce the exact same results.
"The open letter is about letting NZ Rugby know that enough is enough and we want them to take us up on our offer to support them through this process. As much as New Zealanders love rugby - we need New Zealanders to respect women."
Other signatories included Sexual Violence Survivors advocate Louise Nicholas, MPs Jan Logie, Ruth Dyson and Tracey Martin, social justice advocate Catriona MacLennan and Barbara Williams of the National Council of Women.
Tew said NZR would speak with Blue "as a priority on what more we could do".
"By way of context, in recent years, New Zealand Rugby has ramped up programmes that provide education for players as they enter our environment," Tew said.
"These include our induction programmes for professional players which deliver modules relating to risk awareness and their heightened responsibility as public figures, social media, healthy relationships and mental well-being."
NZR was expanding the work, developing a "respect and responsibility education programme" focused further on healthy relationships and consent issues.
It has also begun advertising for a "respect and responsibility manager" to lead it, and is working with six other codes.
The letter followed earlier rebukes by Prime Minister John Key and All Blacks coach Steve Hansen yesterday, both saying that lessons had to be learned from it.
"We are brought up in New Zealand to have respect for women," Key said. "So I would hope the Chiefs would quietly just step back and learn from that."
Asked about the report, Key said he had not read it fully but doubted NZR would have tried to sweep it under the carpet. "I think they would see the severity of the situation."
He said he agreed with Hansen there was no place in the sport for such events.
