A head teachers' conference has heard claims of threats such as dead animals being left in school playgrounds.
"Trojan Horse has not gone away," said Sarah Hewitt-Clarkson, head of Anderton Park School in Birmingham.
Responding to the claims, Education Secretary Nicky Morgan said: "There is no place for extremism in our schools."
The National Association of Head Teachers' annual conference in Liverpool heard warnings that problems over extremism remained unresolved and schools could still face pressure on issues such as tackling homophobia.
The so-called Trojan Horse inquiries followed allegations that there were organised attempts by hardline Muslim groups to undermine head teachers and take over schools in Birmingham.
Head teachers at the conference complained that no governors had been barred as a result of the inquiries and they called for a database which would identify individuals removed from governing bodies.
Ms Hewitt-Clarkson told the head teachers' conference: "Trojan Horse has not gone away. Those of us who were involved, we knew it was the tip of the iceberg.
"We still have dead animals hung on the gates of schools, dismembered cats on playgrounds. We have petitions outside schools, objecting to teachers teaching against homophobia."
There were threats on social media, she said, such as "Any head teacher who teaches my children it's alright to be gay will be at the end of my shotgun."
Ms Hewitt-Clarkson said she knew of a school which had found a dismembered cat in the playground, while another had a dog hanging from the railings.
Head teachers warned that despite the high profile reports following the Trojan Horse claims, the response had been inadequate.
Alison Marshall told the conference: "Despite all the evidence we have, we're faced with a situation where not one single governor implicated in the Trojan Horse scandal has been investigated or even banned. Where is the justice in that?"
And Ms Hewitt-Clarkson warned that the problems underlying the Trojan Horse claims could "start up again".
"All the behaviours and things we saw before are still there. So too have promises that have been broken," she told the NAHT conference.
There were particular concerns about the lack of scrutiny over the role of governors, highlighted by the Trojan Horse inquiries.
Tim Gallagher told delegates the lack of regulation meant it was "blindingly obvious" that there would be problems with governing bodies.
"Many, many of our members have suffered greatly from rogue governors," he said.
The conference carried a motion calling for a national register of governors who have been removed or barred so that schools and local authorities can check the suitability of governors.
The BBC revealed earlier this year that there is no central record of governors held by the Department for Education, which would also show people serving as governors in multiple schools, one of the concerns raised in the Trojan Horse inquiries.
Mrs Morgan, responding to the heads' warnings, said: "There is no place for extremism in our schools and we continue, absolutely, to work to eliminate any form of extremism."
But the Conservative education secretary said: "This is a reminder that this is a serious issue and something that is not going to be solved overnight.
"We have taken action to remove and continue to take action to remove people from being in schools who don't follow British values."
Head teachers have warned that intimidation is still continuing after the investigations into the so-called Trojan Horse scandal.