Are you sure about that?
When masks were introduced the message justifying them firmly centred around reducing transmission. It feels to me rather that the rather nebulous “viral load” argument is being used as a way of shifting the goalposts because, as you say, it’s now inconveniently obvious that masks have little to no effect on transmission. What is the new evidence on viral load, out of interest?
In general terms people who are exempt may well have a disability, which means they do have a right to access transport, services subject to reasonable adjustments. In the case of a taxi the taxi company might make adjustments to the vehicle (or send a bigger vehicle to better enable distancing). But the onus is on the provider to make these adjustments. Simply refusing to carry passengers who are exempt is skating on very thin ice.
By contrast there is no absolute right to not be infected with a highly communicable, airborne disease. How could there ever be? The harsh reality is that some people (I’m one of them!) do jobs which cannot be done from home, and might put them into situations where they are at more risk of catching the virus. Ultimately people doing these jobs have the choice of either continuing to do them, or doing something else instead, or giving up work and having no income.
We do need to get away from the emotive talk about safety etc. In this context. A taxi driver who is under 45 is far more likely to die in a car crash than they are of Covid so refusing to carry mask less passengers while still being prepared to drive a car around to earn a living is irrational.
Again, if we differentiate between belief in the efficacy of masks, and the scenario outlined in posts above.
Whether or not we wear masks, we are ALSO supposed to maintain social distancing. The waiter did get it wrong in that event, because they chose to do their job in a way that unnecessarily exposed both them and their customers to greater risk of transmission when there were reasonable alternatives available as a way of doing their job. That, due to their exemption, they were maskless compounded the error; fortunately, the understanding of the transmission of this virus suggests that the absolute change in risk would have been very limited.
That brings in the question of viral load. In general news reporting, I have seen reference to viral load for some months as a possible explanation of differences in case severity and transmissibility. As I understand it, the way the Covid virus infects is partially dependent on dose, meaning that shorter exposure and/or more distant contact will reduce the impact on the person infected; a high dose of the virus being associated with more severe cases. The taxi driver in this scenario is not being entirely irrational; doing a job that must expose him to heightened risk because of his proximity to others, seeking to follow measures that the government are telling him are beneficial is an entirely rational response to risk. It may not, however, be a proportionate or reasonable response to that risk, even if the person with an exemption doesn't have protection under the Equalities Act.
As an aside, the case for face coverings (and I use the term to distinguish from medical masks of whichever grade) has long included the reduction in dose resulting from the filtering effect provided by those coverings. It is not new news - I recall reading of it back in the spring.