The families of two British men killed fighting Islamic State in Syria have condemned a report urging the government to treat those who join Kurdish forces in the region as potential terrorists, insisting their sons should be remembered as heroes.

The report by the Henry Jackson Society suggests that British volunteers who travel to Syria to join the Kurdish People’s Protection Units (YPG) could pose a “domestic security risk” upon their return to Britain.

Entitled The Forgotten Foreign Fighters: The PKK in Syria, the paper says that the US-backed YPG is linked to the outlawed Kurdistan Workers’ Party (PKK), which has waged an insurgency against the Turkish state for autonomy since the 1980s. The YPG, however, denies any perceived links to the PKK and is not considered a terrorist group by the US or UK.

It goes on to suggest that Britons who join the YPG could “contribute to criminal terrorist activities” of the PKK or risk being recruited by foreign extremist groups to engage in “lone-actor terrorism” on home soil.

But the report has been met with anger by the families of men killed fighting alongside the YPG, who say they are “shocked and hurt” by the suggestion that their sons died in the name of terrorism.

“My stomach is burning with anger,” said Vasiliki Scurfield, the mother of former Royal Marine Kosta Scurfield, from Barnsley, who was the first British national killed in action in Syria on 2 March 2015. “My son was no terrorist. He went out there, in his own words, to fight terrorism, not to support it. He went because he felt the British government hadn’t done enough to nip [Islamic State] in the bud.”

Dean Evans, 22, from Warminster, became the second Briton to die in Syria as he attempted to rescue a fallen comrade during the battle for the city of Manbij on 21 July 2016. His stepfather, Steve Howell, said: “I feel sickened at the thought of Dean being painted as a terrorist. I knew Dean inside out and there’s no way he stood for terrorism. Dean went to Syria to fight against evil, for the sake of humanity.”

He added: “We walk around in this country free to speak, to worship, to live as we like. People under Isis don’t have those freedoms. Dean felt that they had every right as we do to enjoy that pleasure. He didn’t go there to kill people – he said that to me. He said he wanted to put himself between innocent people and terror.”

The report – which also calls on the UK government to urgently prevent its citizens from joining the fight against Isis – profiles 60 foreign volunteers from 12 countries who joined the YPG in Syria and analyses their motivations. Twenty-nine of them have been killed in action.

Scurfield’s mother said the profile of her son was “riddled with inaccuracies”. “If it wasn’t for the fact that [the report] is defaming my son, I’d laugh. It’s a hilarious concoction of various copy and pastes from other people’s articles in order to make a point without any real evidence or primary source material provided.”

She said she had had many discussions with Scurfield about his motivations and claimed that “the word PKK never once passed his lips”. “It’s perfectly OK to pose an academic argument and invite discussion over the relationship between two organisations,” she said. “What’s not OK is to tell verifiable untruths about my son and to piggyback on the media interest generated by his and the other brave volunteers’ deaths.”

A spokesman for the Henry Jackson Society said: “It was certainly not our intention to cause any upset to the families who have been tragically bereaved. The broader point remains that the YPG and the PKK, a proscribed terrorist organisation, are one and the same. The vast majority of YPG British foreign fighters were not aware of this fact. We stand by the research in the report, and the profiles featured are all sourced properly within it.”

While some Britons have been arrested upon returning from Syria, none to date have been prosecuted for joining the YPG, which is not considered a terror group in the UK.

In a statement given to the Guardian, official YPG spokesman Nuri Mahmud said: “We find preposterous reports by some individuals, media institutions and other organisations – including the Henry Jackson Society … claims that the YPG is the same as the PKK, despite the two groups operating in different areas, with different methods and for different objectives. … The YPG is a completely different organisation to the PKK and has no ties to it.”

A Home Office spokesperson said everyone who comes home after taking part in the conflict in Syria and Iraq “must expect to be reviewed by the police to determine if they have committed criminal offences, and to ensure that they do not pose a threat to our national security”.

Scurfield and Evans are among four British men killed fighting Isis since the first volunteers arrived in Syria in the autumn of 2014. Ryan Lock, 20, from Chichester, became the third when he took his own life after his unit was surrounded by Isis fighters on 21 December last year. Then, on 5 July this year, 22-year-old Luke Rutter, from Birkenhead, was killed during an ambush in a suburb of the Isis stronghold of Raqqa.