I don't take my shoes off unless I feel it is necessary or it is requested. Sometimes I do it when I don't need to do it, just to be safe. It is a courtesy. Why take the chance of tracking mud, dirt, grass on somebody's carpet.
Any appraiser who has been doing this for any length of time, should have enough courtesy to do the right thing. If you don't like taking your shoes off, or you think you are above removing your shoes, then I suggest you be prepared with another option. We are getting paid to perform a service, not to soil their home, no matter how bad you think their home is. I prefer to treat all individual equally, even if they are pigs. There are too many people in this society and our industry that think they are better than others and I will not sink to that level.
Seriously, this should not be an issue. If your shoes are not clean, they should not enter the house. The only exceptions I can see are foreclosure properties, REO's, beginning construction (sometimes) and trashed properties that are not occupied. What does everybody else appraise on astroturf?