The freemasons have accused assembly members in Wales of pursuing "class war" against them.
A rule change would mean masons won't be "singled out"
The claim was made as AMs took a step towards changing their rules on declaring membership of the masons.
The proposals would mean that AMs would also have to declare whether they belonged to other clubs and bodies "with restricted membership".
AMs hope that this would avoid the charge that under their existing rules masons are being unfairly singled out.
The assembly's stance on AMs having to declare their masonic membership has long caused problems.
It remains the only democratic body in Britain which insists that masons should declare their membership.
Previous attempts to change those rules - by forcing members to declare all memberships of private clubs - have failed, and now a slightly different resolution is suggested.
But James Bevan, a leading mason in Wales, said he was very disappointed that the assembly had made no progress on the matter after two and half years of dealing with it.
He said the problem was AMs who "aren't prepared to listen to reason, perpetuating some sort of class war that they may have been involved with when they were at university".
Freemasons complain of "myths and misconceptions" about them
Mr Bevan said it was time they grew up, and vowed that the masons would not give up.
While he said masons did not want to begin litigation, they could begin making a legal challenge within months if the assembly threw out the compromise solution again in the new year.
There have been previous warnings of legal action against the assembly over its attempt to force masons into the open.
Labour AMs have also rebelled in the past against plans to compel members of all other societies to declare themselves.
On Thursday, the assembly's standards committee tried to find a new way forward.
It agreed to ask AMs to vote on changing the rules so that members of clubs where membership is restricted must declare their interest.
Because this would change the assembly's standing orders, it would need a two-thirds majority.
The committee was given legal advice suggesting that its current policy applying only to masons could be challenged in the courts because it could be discriminatory, and in breach of the European Human Rights Act.