Equalities law does not give you a right to enter commercial premises without a mask if the business directs you to wear one.
Until/unless this is tested in court we don't know that but I'd be very surprised if Costco won such a case.
The 'reasonable excuses' in the legislation specifically refer to people who cannot put on, wear or remove a face covering because of a disability within the meaning of section 6 of the Equality Act 2010. Also to those accompanying or providing assistance to someone who relies on lipreading.
www.legislation.gov.uk/uksi/2020/791/regulation/4
The explanatory memorandum that accompanies this legislation states:
7.6 Exemptions from this requirement exist for members of the public with a “reasonable excuse” for not wearing a face covering. A non-exhaustive list of circumstances in which a person has a reasonable excuse is set out in regulation 4, and generally relate to medical and equalities grounds. ... Nobody who has a reasonable excuse as set out in regulation 4 and is therefore not wearing a face covering should be prevented from visiting a shop or supermarket or other setting covered by these Regulations.
And also:
12.2 The Department has considered the fact that some people may be deterred from visiting the relevant settings where these Regulations apply due to them being required to wear a face covering either because they cannot source a suitable face covering or they have protected characteristics (e.g. a disability) which makes it difficult to wear a face covering ... The Department has also included a range of exemptions to ensure that this policy does not unfairly discriminate against those with protected characteristics. Furthermore, the policy will be supported by a communications campaign that will make clear that some people are exempt from these regulations and people should not be challenged by members of the public for not wearing a face covering.
(my bold)
www.legislation.gov.uk/uksi/2020/791/memorandum/contents
And, as has already been noted, the guidance on the government website also says that nobody who is exempt from wearing a face covering should be denied entry to a shop, public transport or other 'relevant place'.
So it's very clear that the government intends the exemptions to function, in part, as a reasonable adjustment to prevent unfair discrimination against disabled people. My understanding is that where legislation is not 100% clear, the government's intentions carry a lot of weight in court.
If a shop or other 'relevant place' decides not to honour the exemptions - 'No mask, No entry, No excuse!' - then this has a huge and disproportionate impact on some disabled people. It's indirect discrimination which is only lawful if it's a proportionate means to achieve a legitimate aim.
Nobody's arguing that preventing the spread of the virus is not a legitimate aim. The argument is about whether denying entry for some disabled people to shops, public transport and pretty much all other indoor public spaces is a proportionate means of achieving that aim.
Costco would have to argue that masks alone make so much difference to the spread of the virus that they are justified in ignoring government guidance and refusing entry to some disabled people because they are unable to wear a face covering.
I think they'd find that very difficult because masks only make a bit of difference, just like washing hands makes a bit of difference, 2M distancing makes a bit of difference, all the convoluted and ever changing rules on social gatherings, which businesses are allowed to open until what time and whether they must serve a scotch egg, who's allowed in our homes or gardens, how long we must isolate or quarantine ... bla bla bla. All the measures make a bit of difference and we need all of them and we need the majority of people to comply with each of them but there has never been (in the modeling) an expectation of 100% compliance with any of them.
And, as we are discovering, even tier 4 restrictions are nowhere near enough to contain the new variant because schools are open and they are not safe, and people still have to take public transport to spend hours each day in their supposedly 'covid-secure' workplaces.
That's the background against which we should judge whether it's proportionate to refuse entry to all public indoor places, as well as public transport, for disabled people who are unable to wear a face covering, for the foreseeable future.
Clearly that's massively disproportionate.
That's before we even consider Costco's concession of allowing those who are unable to wear a mask to wear a visor instead, which goes against not only government guidance but also scientific consensus. This is hygiene theatre which calls into question what their legitimate aim is in the first place.
TBF, the government's main stated aim for the face covering legislation was to increase consumer confidence. Preventing infection was only ever secondary. This is evident in that prick Hat Mancock's speech as well as in the explanatory memorandum:
www.gov.uk/government/speeches/face-coverings-to-be-mandatory-in-shops-and-supermarkets-from-24-july
www.legislation.gov.uk/uksi/2020/791/memorandum/contents
See also the government guidance, still live when the legislation came in, on how to make a 'face covering' out of a single layer of old t-shirt:
<a class="break-all" href="https://web.archive.org/web/20200714162332/www.gov.uk/government/publications/how-to-wear-and-make-a-cloth-face-covering/how-to-wear-and-make-a-cloth-face-covering" rel="nofollow" target="_blank">web.archive.org/web/20200714162332/www.gov.uk/government/publications/how-to-wear-and-make-a-cloth-face-covering/how-to-wear-and-make-a-cloth-face-covering
Consumer confidence is a legitimate aim for a business but if that's what Costco are relying on then their discriminatory policy looks even more disproportionate.