Face coverings are mandatory on buses and trains and in inside public spaces such as shops and workplaces – which is expected to continue until at least next year.
However, those with some health conditions and disabilities are exempt, such as autism, dementia, learning disabilities and severe anxiety.
The charity Scottish Autism said it was aware of some autistic people being verbally or physically abused over not wearing masks.
William Rae, from Aberdeen, told The Scotsman he regularly received comments, including that he should not be out without a mask
The 33-year-old office cleaner, who suffers from autism, anxiety and asthma, said: “Being on public transport without a mask, sometimes I get weird looks and people try to avoid me.
"I also notice people saying to others they wonder why I can't wear a face mask.
"It's not just public transport – on a weekly basis when I go to supermarkets, I get strange looks, and have even had people say to me ‘you shouldn't be out if you can't wear a mask’.
“I explain to people that I can't wear a mask because of underlying health conditions, but they have replied ‘well, there are emergency services and other professionals with exactly the same health conditions as you, but they can wear a mask’.
“I would simply ask people to think why can that person cannot wear a mask and what can they do to make their experience better?”
Scottish Autism deputy chief executive Charlene Tait said: “While we all appreciate the importance of wearing a face mask to reduce the spread of Covid, sensory processing differences can cause serious issues with mask wearing for some autistic individuals.
"The Autism Alert card [which Mr Rae has], endorsed by the Scottish Government and Police Scotland, provides an ideal means for those exempted from having to wear a face mask to identify themselves.”
Nick Ward, director of the National Autistic Society Scotland, said: “Many of the 58,000 autistic people living in Scotland are comfortable wearing face coverings. However, some cannot wear one through no fault of their own.
"Many autistic people face sensory challenges and so face coverings for some can be distressing.
“It’s important that members of the public and those working in shops and on public transport be aware of that and act sensitively when they see someone not wearing a face covering.”
Anthony Smith, chief executive of passenger watchdog Transport Focus, said: “It’s important people who are exempt can travel without fear of confrontation.”
Joseph Carter, head of Asthma UK and British Lung Foundation Scotland, said: “Despite the clear message that some people with medical conditions are exempt from wearing face masks, our helpline has received many calls over the course of the pandemic from people who have faced prejudice from other members of the public for being without one.
“We hope that as the stay at home order is lifted and shielding begins to come to an end, people will keep William and others like him in mind, and ensure no-one faces any more prejudice during this already very stressful time.”