Many people know that oil and water don't mix, but ignorance of the underlying principles contributes to the spread of AIDS and other sexually transmitted diseases.  To understand this, we recall that nonpolar compounds, such as oils, are insoluble in polar solvents, such as water.  Most nonpolar liquids dissolve in one another, and many polar compounds dissolve in polar liquids.

In a 1990 report, the Kinsey Institute for Research in Sex, Gender, and Reproduction reported that half of Americans 18 years and older do not know that oil-based lotions and creams, such as baby oil, petroleum jelly, and many hand lotions, should not be used with Latex condoms or latex diaphragms.  These lubricants all contain nonpolar compounds and dissolve latex, which is also nonpolar, in as little as one minute. Only a small and essentially undetectable amount of latex is dissolved, but condoms are so thin that this amount is enough to allow the passage of sperm or the HIV virus without detection, increasing the odds of unwanted pregnancies and the spread of diseases.

Even those who know better than to use oil-based lotions as lubricants often confuse "water-based" and "water soluble" lotions.  Some products can be washed away easily with water, but they also contain mineral oil.

Lotion manufacturers add surfactants to oil-based lotions to make the lotions water soluble.  Surfactants are special chemicals that are soluble in both polar and nonpolar substances.  As an example, soap has the ability to mix with oil and water to produce an emulsion of soap, water, and oil.  The presence of surfactants in oil-based lotions allows these lotions to be rinsed away with plain water, just as soap allows us to wash away oily grime with water.  Water-based lotions can therefore contain mineral oil and other nonpolar substances which can still dissolve latex.

Whitten/Davis/Peck:  General Chemistry with Qualitative Analysis,  5/e,  p. 505