The Rasen Mail contacted Morrisons for a statement.
A spokesperson said: “We’re following government guidelines on face coverings.
“Those who are offered a face covering and decline to wear one won’t be allowed to shop at Morrisons unless they are medically exempt.
“To help with shopping in store, we offer a Sunflower Lanyard to those who would like to take one on entry so that colleagues inside the store are aware the customer is medically exempt.”
The Rasen Mail also contacted Lincolnshire Co-Op which has stores in Market Rasen, Caistor and Wragby.
A spokesperson for Lincolnshire Co-op said: “We want everyone who is able to wear a face covering to abide by the law.
“Throughout the pandemic, we’ve followed official government guidance which in this case, asks retailers to encourage compliance.
“We do so through signs at the entrance and inside stores and have regular reminders on in store radio.
“When the law came into force, we also gave away face coverings in all our food stores to encourage compliance and we have done this on several occasions since.
“We want our colleagues to feel safe at work and so we don’t require them to challenge customers without a face covering if they aren’t comfortable to do so because this can bring about the potential for both verbal and even physical abuse.
“We are happy for colleagues who feel confident to politely remind customers that they should wear a mask and offer a free disposable mask where appropriate - though it is also important to recognise that there are people who are unable to wear a face covering and our teams are asked to be mindful of this.
“Legally, customers with exemptions do not have to provide proof of this.”
Market Rasen Pet Centre, in Queen Street, is owned by Bridget Pitman-Brand.
She says that although there are signs stating customers should wear face coverings, she will not refuse anybody who chooses not to.
She said: “We are very lucky all of our customers have worn masks without us having to ask them to.
“However, as I said from the start, we have a notice asking people to wear a mask on the door.
“Should someone come in without one on, I will not refuse to serve them.
“None of us can afford to turn away business at any time but right now it is even harder and small shops need every penny.
“Thankfully, I have not been put into that position and all my customers have been amazing during this very difficult time.”
The Rasen Mail also contacted West Lindsey District Council for a comment on how the issue is affecting the whole district.
A spokesperson said: “The Council cannot take any action against a business who refuses entry for this reason - this is a civil matter between the individual and the business.
“The Council, as part of its ongoing work in relation to Covid 19, is monitoring businesses to ensure that they are encouraging customers to wear masks and that they have the appropriate signage in place.
“To date most businesses have been very reasonable in their approach to exemptions.
“However, if you are exempt and not wearing a mask, you can expect to be asked about this.”