Don't have a good indicator of how many people would worry about public data,

Some people are easier to identify than others (for example, if you're female or from a particular country) and any person may feel uncomfortable about a particular question, so that even marginal concern about being identified with an odd view may skew results.

Consider making the data public in a way that gives the complete set of answers to each question, but doesn't allow comparison of how one person answered multiple questions. (I'm sure there's an easy way to say this, I don't know it.) So in other words, you can't tell that the person who answered "karma = -16" also answered "yes" to "superstitious".

Any cross-correlations, of course, would need to be computed using the original, publicly unavailable data.