Senior police officers have urged local authorities to help reduce the number of protests and counter-protests held across Scotland.
In a strongly worded letter, Police Scotland divisional commanders said such events posed public safety risks due to coronavirus.
However, they accepted many protests were "entirely legitimate".
In recent weeks, police have handled clashes between anti-racism protesters and opposing groups at demonstrations.
On one occasion, violent scenes escalated after a far-right group gathered in Glasgow's George Square to "protect the Cenotaph".
They arrived shortly before a planned demonstration against the evictions of asylum seekers.
Some councils have already seen planned demonstrations scrapped in light of the pandemic.
The Orange Order's annual 12 July celebration has been cancelled for the first time since World War Two.
Divisional commanders are chief superintendents in charge of local policing in divisions.
Their letter said protests and counter-protests have often required "significant resource deployment" from the police, meaning officers are taken out of their local area and are unable to attend to other demands.
It said the issues and grievances being aired are often rooted in "wider social and political issues", and can act as proxies for "ingrained sectarianism".
"Protecting the safety of the public is paramount and all Police Scotland operations are planned and conducted with this in mind," it read.
"We live in a democratic society and police have a duty to protect the rights of both individuals and groups who wish to peacefully protest or counter-protest.
"But this has to be balanced against the rights of others who might be impacted upon by such activity and will not accept or tolerate violence and thuggery."
The letter cited a range of issues handled by police including the mass stabbing in Glasgow on 26 June.
Six people including PC David Whyte were injured in the knife attack in the Park Inn hotel before the suspect was shot dead by armed police.
Divisional commanders said the incident "highlights the risks" that police officers face daily.
They also pointed to the ongoing duties of the force - such as "proactive patrols" of beer gardens - as the country moves from Phase 2 to Phase 3 of the lockdown.