If you can't be open and honest about any medical issues, past or present, don't bother applying. Not only are you lying (not a trait looked upon fondly in the CF), but if these sensitive issues arise again 1,5,10 years down the road, and you are no longer employable, then we have wasted time and money training you.
However, the CF doctors, like all doctors, take the privacy of the individual seriously. If you tell the doctor the issue, they will take it into account when making their medical evaluation. It may stay in your medical file if you go further through the process, but only the medical staff who access your file would know the information, just like in any civilian medical organization.
There is also nothing so sensitive that our doctors haven't seen before.