The DUP has asked the Ancient Order of Hibernians to explain why an "unrepentant republican" who said Catholic judges would be dealt with as "collaborators" has become one of its senior elected officials.
Former Executive Minister Nelson McCausland said former IRA prisoner Gerry McKeough - who now opposes Sinn Fein - would be leading one of the annual AoH parades next Monday.
And party chairman Lord Morrow said McGeough's remarks were a "blatant hate crime" the PSNI should investigate.
Mr McGeough (57), who was elected county president of the AoH in Tyrone in March, was severely criticised after calling Catholic judges and prosecutors in Northern Ireland "traitors"".
TUV leader and senior QC Jim Allister said the comments - in an US radio interview - "require to be investigated as incitement".
And Ulster Unionist Ross Hussey commented: "What is truly pathetic is Mr McGeough desperately clinging to an ideology that has long been discredited."
Mr McGeough was previously elected as AOH president in Tyrone some years ago but then jailed for the attempted murder of former DUP councillor Sammy Brush in 1981. He was sentenced to 20 years in jail, but released after two under the terms of the Good Friday Agreement.
Interviewed by WBAI radio in New York at the weekend, he said: "There are people from republican families who are sitting as Diplock court judges, and prosecutors... and they are arrogantly passing judgement on patriots. So you have Irish Catholics, traitors in effect, administering British rule here in the six counties. We want [the British] out and then we will deal with all these other issues... the collaborators and all the rest of it."
North Belfast MLA Mr McCausland said: "What other fraternal organisation, Protestant or Catholic, would have a convicted gunman and clearly an unrepentant one as a county president or grand master?"
There was no immediate response from the Ancient Order of Hibernians.
Policing Board member Mr Hussey added: ""Just as the IRA had a deliberate policy of targeting Catholic RUC officers in a bid to deter others from joining, so the IRA actively targeted Catholic members of the judiciary, such as Tom Travers, whose daughter Mary was murdered in 1984."
On social media, Judge Travers' daughter Ann said there had never been any justification for killing Catholics, or anyone else, working in the judiciary, security forces or civilian support staff. They were not traitors and they gave more to this country than [armed republicans] ever have or ever will," she said.