I would not conduct any business of any sort with anybody who presented themselves to me in a full face mask. Whether or not it is safe or hygenic for them to do so is irrelevant. It is rude, bad mannered and discourteous to expect anybody to have dealings with you when you are so dressed.
Turning to the particular issue of the medical profession, I am fortunate to not have much dealings with “sawbones” but when I do I usually have difficulty understanding what is being said to me anyway as most of the practitioners I encounter seem not to have very good English. If they had they faces covered I would be denied the ability to see their expressions and read their lips. The comparisons with surgeons and the like wearing their medical masks when undertaking surgery is not appropriate. They have to wear their masks to prevent infection, but whenever they can they speak to their patients without their masks on.
There is no need for any “compromise” on this issue. The overwhelming majority of people in the UK do not deal with each other with their faces covered. It is not customary, it is unnecessary and offensive to do so. People wishing to work in the medical profession (or indeed in any other business) who feel it necessary to deal with people whilst masked up should consider whether they are really living in a part of the world that best suits their requirements.