Our County assessor's office will allow the transfer tax to be blocked during recording provided there is a letter from all parties prior to the recording. We do not see much of this in our area but there are some sellers of exclusive property that benefit from this.
In the majority of the USA, real estate transactions are a matter of public record; obviously you must be in one of those states. Zillow (et al) receive and aggregate their info from public databases, ergo, there's nothing you can do about it... Sorry!