Folau has been found guilty of "high level" misconduct for his controversial social media post condemning gays and others to hell. The Wallabies star is yet to hear the verdict on his $4m contract.
Jones has been a staunch supporter of devout Christian Folau throughout a saga that has divided Australia, mainly on the issue of freedom of speech and allowing a person to air their religious beliefs.
Jones used his latest hard-hitting column in The Australian to condemn Rugby Australia's "mindless prosecution" of Folau, calling on chief executive Raelene Castle and her board to resign for their handling of the affair.
"The sadness in all this is not Israel's alone. He is a gifted and gentle soul with not a sinew of hate in his body," Jones wrote.
"While he is at peace with his god he says to me, simply and plaintively: 'They make me feel like a murderer.'
"Yet even murderers and rapists get a reduction in their terms."
Jones quoted a rugby fan's frustration at the situation: "Our reputation as a great sporting nation is going down the tube … why does a guy who, with a punch, breaks another player's jaw get banned for six weeks, yet a guy who says something that others don't like gets banned for life?"
Jones likened the current debate on religious freedom highlighted by the Folau case to to that on abortion.
"The intractable debate over abortion has raged for decades. Both sides are outspoken, publicly and privately, and not shy of protesting to promote their views. The conflict of opinions on this issue is also equally as personal as someone's sexuality; after all, it deals with a woman's body. The debate is also potentially hurtful and involves religious views given that much of the objection to abortion is based on religious beliefs.
"Yet somehow society is able to incorporate these opposing views, and the expression of them, one largely religious, the other not, without calling for those who express the possibly unpopular religious view to be sacked.
"Why is the same tolerance not extended to Folau's recitation of extracts from the Bible?"
Jones felt Rugby Australia's inability to sort out a proper clause in Folau's contract around this issue left them with no alternative but to fall on their sword.
"Given that it appears they won't admit they are wrong and given that rugby and its proud legacy are being destroyed, the board should simply say, this is a problem we don't believe we can satisfactorily resolve, nor, we believe, should this be pursued to its ultimate legal conclusion," Jones wrote in The Australian.
"The board can yet salvage something in the interests of the game.
"Resign graciously. Allow a new administration to address all the problems of the game, including this, and start again on an equal footing honouring the twin principles of fairness to everybody and the preservation of our game.
"Where we are today can be simply expressed. It is either goodbye the board of Rugby Australia or goodbye democracy and goodbye freedom. This must stop before it gets worse."