Here is a summary of findings by a paper which suggests that the vast majority of genetic counselors tend to err on the side of protecting a mother's privacy if her husband is not the father of her child. Here is an important point though:
It is much more likely that bringing up the possibility prior to testing will put the woman in the very position we are trying to protect her from. ... If, as I have suggested, the counselor plans to attempt to keep paternity but not personal genetic information from the man, it is probably better not the discuss the issue ahead of time.
The problem is pretty obvious, for autosomal recessive diseases like Cystic Fibrosis both parents need to be a carrier. There have been instances when "fathers" found out they weren't carriers, and that is how they discovered that their child was not their biological offspring (this is not a non-trivial consideration when medical expenses can result in a great deal of debt and the biological father is absolved of any financial responsibility). But there is another angle which is important: a man who is ignorant of the ramifications of autosomal recessive diseases and the ease of paternity checking status is likely to be dull in the first place. Additionally, cross-cultural data tends to show that high socioeconomic status males are much more confident of the fidelity of their partners, and have reason to be, paternity misassignment for these males is as low as 1%.^1 On the other hand, lower socioeconomic males tend to be cuckolded far more often. In the future relatively cheap and ubiquitous genetic screens will make one's autosomal recessive status something that most individuals will be aware of, at least abstractly, but the less intelligent males are probably the ones who won't do the punnett square. Wondering how dull some low SES males can be? Watch the video below the fold.... I do not believe this is actually a "true story." Nevertheless, any remote shred of plausibility would disappear if we were told that the man was an investment banker or doctor. 1 - This can be confirmed by the relatively high fidelity of elite patrilineages in the historical record.